Science Mundi

Graph Numbers and Distance Related Parameters of Zero Divisor Graphs

Eliud Mmasi — 2024-08-07

Distance-related parameters have applications in the field of pharmaceutical chemistry, network discovery, robot navigation, and optimizations. Cyclic structures exhibit significant topological features that have become important research areas in the field of computer science and mathematics. Due to the inherent algebraic relationship between graph numbers and distance related parameters, this paper characterizes variants of distance related parameters and graph numbers associated with the zero divisor graphs akin to cyclic structures obtained from classes of completely primary finite rings. In particular, we investigate the local fractional metric dimension and provide certain results concerning graph indices namely the Weiner index and the Zagreb index.

Unethical Practices in Tanzania Public Universities: Does Workload Matter?

Nivad H. Mwilongo — 2024-08-27

Globally, the operations of universities rely on workload distribution. The extent to which the workload shouldered by employees is excessive or insufficient has implications for ethical behaviour and well-being in academic careers. This paper examined the effect of workload on unethical practices in Tanzanian public universities. Karasek's Job Demand-Control Model served as the foundation for the study. The quantitative research approach was utilized, and questionnaires were used for data gathering. The study adopted a correlational research design. The study gathered data from three public universities intending to reach 245 respondents sampled through stratified sampling who were administered questionnaires, and only a total of 209 respondents completed it. The collected data were considered for analysis through descriptive and inferential statistics. Meanwhile, STATA MP version 17 was used for analysis to conduct the multivariate regression model. The finding revealed workload has a significant positive effect on unethical practices, indicating that both excessive and insufficient workload contribute to unethical behaviour among academic staff. The study concluded that although workload in higher learning institutions is a lifeblood of curriculum implementation, it is not fairly distributed and thus affects both individual and organizational operations. Therefore, the study recommends that the universities should play a crucial role in developing and implementing internal workload policies that link with academic integrity to foster high-quality services in university operations.

Students' Subjective Well-Being in Cape Coast Metropolis, Ghana: The Influence of Sex, Parenting Style, and Self-Esteem

Eric Mensah — 2024-09-09

This study sought to determine senior high school students’ level of self-esteem (SE) and subjective well-being (SWB), establish the influence of their sex and parents’ parenting style on their SWB, and determine the effect of their SE on their SWB. The cross-sectional survey research design was used. The study was guided by Life circumstances theory (LCT). Final year senior high school students formed the population. Data was collected from 347 senior high school students drawn from a population of 7,665 in Cape Coast with a questionnaire. The spread of the students and their dispositions led to the use of the proportionate simple random sampling technique to select 347 students from the 10 senior high schools in the metropolis. The instrument used to collect data for this study was a questionnaire. Descriptive (means and standard deviation) and inferential statistics like Independent samples t-test, Analysis of Variance (ANOVA), and PLS-SEM were utilised to analyse the responses. Results indicated students’ SE and SWB levels were high. Further, there was no statistically significant difference in students’ SWB with regard to their sex. There were statistically significant differences in students’ SWB levels with regard to their parents’ parenting styles. Results of the study further indicated that senior high school students’ SE significantly and positively predicts their SWB. It is concluded that even though SE is not the sole determinant of SWB, senior high school students will enjoy their learning, feel part of and connected to their school, have a high purpose of learning, and feel highly efficacious academically (SWB). It was recommended that senior high school authorities in Ghana put in place policies and strategies that will sustain the high levels of SE and SWB. This is very important for the realisation of SDG goals 3 and 4, which are critical for the total development, and well-being of students.

Domestic Violence in Nyeri County, Kenya: What and When?

Lilian Wanjiku Machariah — 2024-12-06

Domestic violence is a worldwide problem affecting many households. Nyeri County, one of the 47 counties in Kenya has, according to reports, experienced a steep increase. Nyeri County has experienced tremendous development, and therefore, changes in terms of education, occupation, and economic activities, making it one of the richest counties in Kenya. With these changes in levels of education, strong cultural adjustments, and increased economic endowment, the expectation is that there should be harmony in the homes. Contrary to that, there is a lot of domestic violence as captured by scholars and the media. This study sought to investigate three things namely; when the violence takes place, the types of violence, and why the violence tales place. The study was underpinned by the frustration-aggression theory and the social learning theory, where descriptive and evaluative research designs were used. The following respondents were sampled to participate in the study: 384 household heads, 12 assistant chiefs, 15 police officers, 30 religious leaders, 12 NGOs/CBOs, 3 Sub-county administrators, and 20 village elders. Primary methods of data collection were questionnaires, interviews, focus group discussions, and observation. Quantitative data was analyzed using SPSS version 26 to give frequency distribution, means and percentages, and findings were presented using tables, graphs, and charts. Qualitative data was analyzed using thematic narrations, with findings presented using narrations and descriptions. The study found out that the cases increase when the farmers receive the coffee bonuses, when learners are going back to school and fees is needed, during the festive seasons and traditional festivities, as well as during the drought season. The study concludes that domestic violence is evident throughout the year, but there are times when the cases increase as a result of conflict in the gender roles. In this case, therefore, the study recommends that there should be a social talk on the gender roles in the study area so as to ease the adamant rise and spread of domestic conflicts related to the various sets of culturally defined and allocated sex roles. Further, there is need to empower both men and women in Nyeri county so that no gender feels threatened by the other. This will go a long way in ensuring that there is peace and stability in families and social relationships.

Updated Vector Autoregressive Model Incorporating new Information Using the Bayesian Approach

Michael Musyoki — 2024-11-07

Vector Autoregressive (VAR) models have been applied extensively in modeling time series due to their high precision when used to forecast. In the VAR development, if we have information up to time t, then a VAR(p) model is fitted. However, if new information at time t + 1, is obtained, then a new VAR(p) model has to be fitted which makes one to go through the process again. Therefore, despite their good performance, a need would arise to incorporate new information that could be obtained after the model has been fitted to update the model instead of fitting a new model each and every time a new information is obtained. This study, therefore, considers incorporating the new information to update the vector autoregressive model of order p using Bayesian approach. First, a VAR model of order 1 is formulated after which this is generalized to the VAR model of order p. We assume that the VAR model is the prior while new information is the likelihood. The performance of updated model is compared with corresponding VAR(p) models and the model is found to perform well based on the small values of the root mean square error (RMSE) in the update and in the prediction for the plots obtained.

Analysis of the Impact of Crude Oil Price Changes on Economic Growth in Tanzania: ARDL Econometric Model

Seth Kenedi Mbwambo — 2024-07-03

Crude oil is a valuable resource for boosting global economic growth. In this regard, this study examined the effect of crude oil price fluctuations on Tanzania’s economic growth from 1989 to 2022. Empirically this study utilized time-series data extracted from World Bank in particular, GDP per capital from World Development Indicators (WDI) as proxy of economic growth and Statistical Review of World Energy for Crude Oil prices. In this study, Renaissance growth theory, Autoregressive distributed lag model (ARDL), Dickey and Fuller tests, The Johansen test for cointegration, Breusch- Godfrey test for Serial correlation LM, Breusch-Pagan heteroscedasticity test, Jarque-Bera normality test, Error Correction Model (ECM), Granger Causality test, CUSUM and CUSUMSQ curves tests were used to analyse the data. This study revealed that crude oil price changes have positive and significant impact on Tanzania’s economic growth. A dollar increase in crude oil prices brings about 0.232791unit increase Tanzania’s economic upturn in the short run. The ARDL results also shows that error correction model (ECM) of -0.1000 (p= 0.0025) is significant with its value, suggesting a moderate speed of convergence to equilibrium after shock. Thus, this study recommends to policy maker and the government to ensure that they use fiscal policies that will reduce the adverse impact of the world crude oil prices hikes, finding other sources of energy and promoting research and development to explore and harness the oil fossils to produce oil and reduce oil importations and increase oil exportations to further increase economic growth.

Promoting Logistics Visibility in Supply Chain and Its Influence on Performance of Manufacturing Industry: A Study on Kenya’s Food and Beverage Manufacturing Firms

Douglas Isaaka Mose — 2024-11-14

This paper sought to examine the relationship between logistics visibility and performance of large food and beverage manufacturing firms in Kenya. The study was anchored on transaction cost analysis theory. The study utilized a cross-sectional research design. The target population was 561 respondents drawn from the 187 large food and beverage manufacturing firms in Kenya. The sampling frame for the study was the human resource managers in each of the food and beverage manufacturing firms since they are the custodians of all the employees in the firms. Using a stratified random sampling, a sample of 228 respondents was selected. A structured and semi-structured questionnaire was used to collect data for the study. Using a 10% of the sample size, the questionnaire was pilot-tested to assess validity and reliability before the actual data was collected. The data was analyzed using SPSS version 27. The data was presented using tables. The findings revealed that logistics visibility significantly and positively influenced performance of food and beverage manufacturing firms. It was concluded that as a result of ineffective embrace of logistics visibility, the manufacturing firms failed to optimize their supply chain towards enhancing performance. The study recommended the essence of logistics visibility as a way of ensuring control of logistics processes among the food and beverage manufacturing firms for better performance.

Forecasting the National Health Insurance Fund Membership Enrolment in Tanzania Using the SARIMA Model

Alfred Tembo — 2024-07-20

This paper aimed at forecasting membership enrolment in the National Health Insurance Fund (NHIF) in Tanzania using quarterly time series data. This study used 88 time series data to fit the seasonal Autoregressive Integrated Moving Average model (SARIMA). ARIMA (3,1,1) (0,1,0)[4] model was built and used for forecasting. The results show that there will be an increasing membership enrolment overtime over the years and no signs of decreasing. Thus, the government, apart from continuing subsidizing the cost of accessing health insurance services, should also improve the National Health Insurance (NHI) coverage to accommodate the increased enrolment and discourage dropouts. In turn, this will help to achieve the Universal Health Coverage (UHC) ultimate aim of ensuring equitable access to essential and manageable healthcare services, regardless of individuals’ financial situations, their location, and personality.

On Some Aspects Of Degenerated Cyclic Codes

Boaz Simatwo Kimtai — 2024-08-06

Degenerated cyclic codes constitute a fascinating area of study within coding theory, offering profound insights into the realm of algebraic structures and their applications in error detection and correction. In this work, we delve into various aspects of degenerated cyclic codes, aiming to provide a comprehensive understanding of their properties and significance. We begin by elucidating the fundamental concepts underlying cyclic codes and their degeneration, establishing a mathematical framework for analysis. Subsequently, we explore the algebraic structure of degenerated cyclic codes, investigating their generator and parity-check matrices, as well as their relationships with conventional cyclic codes. Moreover, we investigate the decoding algorithms tailored for degenerated cyclic codes, evaluating their efficiency and performance under different error conditions. Furthermore, we examine the applications of degenerated cyclic codes in practical scenarios, highlighting their utility in diverse domains such as telecommunications, storage systems, and cryptography. Through theoretical analysis and numerical simulations, we demonstrate the efficacy and versatility of degenerated cyclic codes, thereby emphasizing their significance in modern information theory. Overall, this study contributes to the advancement of coding theory by shedding light on the intricacies of degenerated cyclic codes and paving the way for future research endeavors in this burgeoning field.

Income and Transport Cost: Multiple Responses to Tourists Arrivals in Zanzibar

Gerald Moses Mwasambili — 2024-09-17

The tourism sector plays an important role in the Zanzibar economy and continues to be a leading sector and the main contributor to the national GDP but this sector is faced unprecedented challenges and an existential threat from the impact of the COVID-19 virus. In this regard, this study aimed to analyse the determinants of international tourism demand from the top ten tourist’s origin countries to Zanzibar from 2005 to 2021 and to quantify their influence. In this study Gray’s travel motivation theory, Crompton’s motivations for pleasure vacation theory and Dann’s theory of push and pull factors were used to analyse behaviour of tourists and choice of destination. The study adopted panel data analysis and used long, strong balanced secondary panel data extracted from various sources to estimate the impact of GDP per capita as proxy of income, exchange rates, tourism infrastructure, price of crude oil as proxy of transport cost, consumer price indices adjusted by exchange rates as proxy of relative price and dummy variables to capture effects of Covid-19 and economic recession of 2008 on number of tourist arrivals as proxy for tourism demand in Zanzibar. Regression results of fixed effect model suggested that; at the 0.05 significance level, a one unit increase in GDP per capita results into 1.999 units increase in number of tourist arrivals and one unit increase in transport cost would decrease tourist arrivals by 64.991 units. Coefficients value of dummy variable COVID-19 implies that, on average, the number of tourist arrivals decreased on the year of occurrence of COVID-19 pandemic by 9,539 units. The coefficients of other independent variables exchange rates, tourism infrastructure, relative price and economic recession of 2008 bear the right sign even though they were not statistically significant at 0.05 levels. This study recommends that, the government and other stakeholders to work on marketing Zanzibar tourism product to the high-income countries and to work on reducing transport cost from origin countries to Zanzibar.

An In-Depth Analysis of Demographic Shifts and their Effects on HIV/AIDS Prevalence in Eastern African Countries

Augustino Tile — 2024-07-03

Eastern African countries rank in the top ten most highly infected nations globally. To shed light on this, therefore this study investigated the impact of population dynamics on Human Immunodeficiency Virus (HIV) prevalence using a two-stage residual inclusion (2SRI) regression model to address potential endogeneity. The Hausman Test confirmed endogeneity among the variables, justifying the 2SRI model's application. Key findings indicate that population growth rate, fertility rate, and the population aged 15-64 significantly and positively affect Human Immunodeficiency Virus (HIV) prevalence. The instrumental variable, Children ages 0 to 14 young individual infected by HIV, 15 to 24 newly affected by Human Immunodeficiency Virus (HIV), and Children 0 to 14 living with Human Immunodeficiency Virus (HIV), was validated for strength, demonstrating robustness against weak instrument issues. Results revealed that a 1% increase in population growth rate leads to a 53% increase in Human Immunodeficiency Virus (HIV) prevalence. Additionally, the Dumitrescu & Hurlin Granger non-causality test established that population growth rate Granger causes Human Immunodeficiency Virus (HIV) prevalence. These findings underscore the critical role of demographic factors in shaping Human Immunodeficiency Virus (HIV) prevalence and highlight the necessity for targeted public health interventions to manage and reduce Human Immunodeficiency Virus (HIV) prevalence effectively.

Determinants and Extent of Tax Compliance among SMEs in Arusha City Council, Tanzania

Ephrahim Welnery Mchukwa — 2024-09-03

Taxes have been a nourishing commodity in generating revenues liable for financing governments’ budgets all over the world. This being the fact, this study examined the determinants and extent of tax compliance in SMEs in Arusha City Council which was the specific objective of this study. This was a cross-sectional study which employed a double Hurdle regression model to analyze primary data collected from a sample of 100 SMEs’ owners obtained by simple random sampling to represent the entire population of SMEs owners via questionnaire and analyzed with STATA software version 17. Using the economic deterrence theory to guide the analysis of this study, the analysis found that Male entrepreneurs dominate the SME sector, SME owners understand tax regulations and undergo frequent tax audits. Further, the findings revealed that privately owned SMEs, primarily ran by persons in their mid-30s are flexible with an average workforce of nine employees. Furthermore, SMEs were found to generate feasible profits and fulfill tax compulsions by paying an average tax rate. Moreover, the double hurdle regression model shown that age and profits have negative effect on tax payments, and higher household size of SMEs owners are associated with higher tax payments. Additionally, publicly owned enterprises positively comply with tax. Therefore, given these findings, this study recommends to policymakers to streamline tax procedures and develop a platform to discuss tax rates with tax payers before implementing the planned tax obligations.

Second order Extended Ensemble Kalman Filter with Stochastically Perturbed Innovation

Cavin Oyugi Ongere — 2024-11-22

Studies have shown several forms of non-linear dynamic filters. However, Extended Kalman filters have proved to provide more accurate values of the state of dynamic systems over period of time. Though, the results of estimation by use extended Kalman filters are accurate, there is involvement of computation of high dimension covariance matrix that are very expensive. Although Bayesian methods offer a robust and accurate approach, they are often hindered by the computational complexity involved in computing high-dimensional matrices. This study introduces a new filter, the Second Order Extended Ensemble Filter with pertubed innovation (SoEEFPI), designed to numerically address the inversion of high-dimensional covariance matrices and then stochastically perturbing the innovation. The SoEEFPI is derived from the numerical expansion of the expected values of non-linear terms in the stochastically perturbed Kushner-Stratonovich equation, utilizing a second- order Taylor series expansion. Validation of the SoEEFPI is conducted on a three-dimensional stochastic Lorenz 63 model, with simulations performed using MATLAB software. In the validation process , SoEEKFPII is compared with First Order Extended Ensemble Filter (FoEEF), First Order Extended Kalman Bucy Filter (FoEKBF), Second order Extended Ensemble Filter (SoEEF), Bootstrap Particle Filter, and Second Order Extended Kalman Bucy Filter (SoEKBF). Results indicated that SoEEFPI outperformed the other filters (KBF, FoEEF, SoEEF) across all three variables of the Lorenz 63 model: x₁, x₂ and x₃. While SoEKBF exhibited the lowest root mean square error (RMSE), its computational cost is significantly higher due to the integration of high-dimensional covariance, making SoEEFPI a more desirable option since its covariance computation is performed empirically.

Exploring the Prevalence and Patterns of Media Exposure and Use among Adolescent Generation Z in Secondary Schools in Western Kenya: A Focus on Kakamega, Kisii, and Siaya Counties

Pauline Adhiambo — 2024-10-31

The purpose of this study was to explore media exposure patterns among school-going Generation Z adolescents in Western Kenya, specifically in Kakamega, Kisii, and Siaya Counties. By providing crucial insights into the media habits of these adolescents, the study aims to enhance understanding of youth media behavior and its developmental impacts. The findings could inform educational policies, parental guidance, content regulations, and health initiatives to address issues such as screen addiction and cyberbullying. The study applied Erik Erikson's Psychosocial Theory of Development to explore the media habits of adolescents in an exploratory context. Using descriptive and correlational research designs that included questionnaires, interviews, focus group discussions, and content analysis, data was collected from a sample of 384 learners drawn from a population of 190,555 learners using a stratified random sampling method. Additionally, 56 parents and 48 teachers were selected based on the principle of data saturation. A pilot study conducted in Vihiga County with 42 learners yielded a Cronbach's Alpha coefficient of 0.87. Expert faculty members assessed the instruments for face validity. The study adhered to the Kenya Data Protection Act of 2019, ensuring ethical procedures such as informed consent from principals, participant anonymity, and thorough training for research assistants. The data was analyzed using a mixed-methods approach that combined descriptive statistics for the quantitative data and thematic analysis for the qualitative insights. Findings reveal that Generation Z adolescents have widespread access to media, primarily engaging with social media (38%), with at least 35% using media for over 6 hours, notably on social media and mobile phones. A significant portion (35%) of their media consumption occurs without parental supervision, prominently on social media (40.7%) and mobile phones (28.2%). Media serves dual purposes for these adolescents, with radio and television primarily used for education (32% and 31.8%), while mobile phones and social media are predominantly for entertainment (34.6% and 25%). The study concluded that social media is widely used among adolescent Generation Z learners, with substantial daily engagement and minimal parental supervision. This study recommends implementing digital literacy programs, setting screen time limits, and integrating educational content into popular digital platforms, particularly targeting adolescent Generation Z. Schools should collaborate with content creators to enhance learning through engaging, interactive materials.

Optimization of Drying Parameters for Minimization of Moisture Content in Black Tea Production

Bonface Ochieng Otedo — 2024-11-14

Study focuses on black tea drying process on fluidized bed dryer in tea factories. Tea drying variables considered in the study were air temperature, air velocity and time. The response variable in the experiment was the black tea moisture content. Air velocity was varied between 0.21 m/s and 0.55 m/s. Whereas air temperature was varied between 70 ⁰C and 130 ⁰C. Drying time ranged between 0 minute and 20 minutes. Black tea drying experiment was conducted in the macerated tea laboratory at Sotik Tea Company using the miniature FBD Sherwood Tornado model 501. It took 20 minutes experimental time to lower the dhool moisture from 72% to 3.5%. Experimental data was used to develop black tea drying curve and drying rate. The Box Behnken design under response surface design methodology in Minitab software was used to analyze and optimize the black tea drying variables. The optimum variables were found to be at hot air temperature of 100 ⁰C, hot air velocity of 0.38 m/s and drying time of 12.9 minutes. These drying parameters resulted in a more acceptable black tea moisture content of 3.5% db which falls between the acceptable black tea moisture content of 3% db to 4% db.

Effects of Value Added Tax (VAT) Knowledge on SMEs Performance and Factors Affecting SMEs Performance in Morogoro Tanzania

Stephen Bishibura Erick — 2024-07-17

Small and Medium-sized Enterprises (SMEs) play a crucial role in driving economic growth and development in Tanzania. However, the performance of SMEs is hindered by various factors, including the challenges posed by value-added tax (VAT). This study investigates the effects of VAT knowledge and other factors on the performance of SMEs in Morogoro, Tanzania. The research objective is to provide a comprehensive understanding of the key determinants influencing SME success and growth in the region. The study assesses the level of VAT knowledge among SME owners, examines the relationship between VAT knowledge and SME performance, and analyses the impact of factors such as business location, initial capital investment, years of experience, and type of business on overall SME performance. The supply and demand theory are employed as the theoretical framework to understand how changes in costs, induced by VAT, affect the supply decisions of SMEs and consumer responses to price changes. Despite government efforts to address challenges faced by SMEs through regulatory simplification, tax reforms, and digitalization, the performance of SMEs continues to be hindered by VAT-related administrative costs, pricing, and forecasting customer needs. This study aims to fill the research gap by providing valuable insights and recommendations for policymakers and business stakeholders to foster a supportive environment that promotes the sustainable growth and development of the SME sector in Tanzania.

Examining microfinance loan repayment challenges and procedures by small business owners: The case of Vikenge Village, Morogoro, Tanzania

Gabriel V. Komba — 2024-08-31

The research surveys the factors affecting the ability of small business owners in Vikenge village to refund microloans. This study uses institutional theory framework to investigates the constraints encountered by these firms, their means for handling these constraints, and offer hints for improvement. Applying a qualitative research design, semi-structured interviews were performed with 13 small business proprietors. Participants were purposively selected due to their experience in microfinance lending and efficient reimbursement. Through thematic analysis, substantial issues concerning repayment challenges, techniques, and recommendations for enhancement were proven. The survey reveals a variety of obstacles that influence the repayment of loans, for instance; unexpected events, personal and familial matters, fluctuations in the economy, seasonal fluctuations in business, and complications with cash flow. Methodologies to repayment include strategies like saving money daily, options for flexible repayment, clear communication, and seeking outside financial assistance. Survey respondents also offered supportive recommendations, such as using loans for their intended purposes, decreasing interest rates, allowing more flexibility in repayment schedules, providing enhanced customer education and support, ensuring loan amounts are appropriate, and improving monitoring and collection procedures. This research survey enhances value to the current body of knowledge by delivering detailed analysis on the repayment of microfinance loans in small businesses in Vikenge village. The results proposed practical recommendations for microfinance institutions to acquire tailored repayment strategies that meet the varied requirements of borrowers, eventually leading to improved financial accessibility and long-term viability.

The Influence of School Curriculum Support Materials on Academic Self-Concept of Pupils in Primary Schools in Informal Settlements in Kibra Sub-County, Kenya

Grace Wandia Gatundu — 2024-07-30

This study investigates the influence of curriculum support materials on pupils' academic self-concept in primary schools located in informal settlements in Kibra sub-county, Nairobi County, Kenya. Self Determination Theory guided this research. The study employed a survey research design. The target population comprised 138 head teachers, 203 teacher counsellors, and 9536 learners in Class VII, totaling 9877 respondents, from which a sample of 385 respondents was determined using Yamane’s formula. Questionnaires were used to collect data from learners in Class VII, as were interview guides for head teachers and teacher-counsellors. Piloting was conducted among 38 respondents from primary schools in informal settlements in Kibra sub-county to establish validity and reliability. The opinions of educational psychology professionals were used to confirm the study's validity. The split-half method was used to calculate reliability, and the reliability coefficient (r = 0.728; p<0.05) at the 0.05 level of significance revealed a high degree of internal dependability. The findings indicated that there was a significant statistical relationship between curriculum support materials and academic self-concept of r=0.539, p=0.002<0.05. The study concluded that levels of pupils’ academic self-concept in primary schools in informal settlements can be enhanced through provision of curriculum support materials. The Ministry of Education should enforce a policy that all schools in informal settlements should comply with standards for child-friendly school environment. The main beneficiaries of this study will be learners in the primary schools in the informal settlements when the policy makers improve in the provision of curriculum support materials hence their academic self-concept will be enhanced.

Analysis of Adjacency, Laplacian and Distance Matrices of Zero Divisor Graphs of 4-Radical Zero Completely Primary Finite Rings

Frank Omondi Ndago — 2024-08-06

This study is an extension of our study on matrices of zero divisor graphs of classes of 3-radical zero completely primary finite rings. It focusses on Matrices of a class of finite rings R whose subset of the zero divisors Z(R) satisfies the condition (Z(R))⁴ = (0) and (Z(R))³ = (0) for all characteristics of R that is; p, p², p³ and p⁴. We have formulated the zero divisor graphs Γ(R) of R and associated them with three classes of matrices, namely, the Adjacency matrix [A], the Laplacian matrix [L] and the Distance matrix [d_ij]. The study has further characterized the properties of the graphs Γ(R) and the matrices mentioned.This study is an extension of our study on matrices of zero divisor graphs of classes of 3-radical zero completely primary finite rings. It focusses on Matrices of a class of finite rings R whose subset of the zero divisors Z(R) satisfies the condition (Z(R))⁴ = (0) and (Z(R))³ = (0) for all characteristics of R that is; p, p², p³ and p⁴. We have formulated the zero divisor graphs Γ(R) of R and associated them with three classes of matrices, namely, the Adjacency matrix [A], the Laplacian matrix [L] and the Distance matrix [d_ij]. The study has further characterized the properties of the graphs Γ(R) and the matrices mentioned.