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Total coalitions in graphs


Saeid Alikhani
Davood Bakhshesh
Hamidreza Golmohammadi

Abstract

We define a total coalition in a graph G as a pair of disjoint subsets A1, A2 ⊆ A that satisfy the following conditions: (a) neither A1 nor A2  constitutes a total dominating set of G, and (b) A1 ∪ A2 constitutes a total dominating set of G. A total coalition partition of a graph G is a  partition Υ = {A1, A2, . . . , Ak} of its vertex set such that no subset of Υ acts as a total dominating set of G, but for every set Ai ∈ Υ, there  exists a set Aj ∈ Υ such that Ai and Aj combine to form a total coalition. We define the total coalition number of G as the maximum  cardinality of a total coalition partition of G, and we denote it by Ct(G). The purpose of this paper is to begin an investigation into the  characteristics of total coalition in graphs.


Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606