Ordering n-vertex cacti with matching number q by their spectral radii

Abstract

A connected graph G is a cactus if any two of its cycles have at most one common vertex. Denote by C_n,q the set of n-vertex cacti with matching number q. Huang, Deng and Simic [23] identified the unique graph with the maximum spectral radius among 2q-vertex cacti with perfect matchings. In this paper, as a continuance of it, the largest and second largest spectral radii together with the corresponding graphs among C_n,q are determined.  Consequently, the first two largest spectral radii together with cacti having perfect matchings are also determined.

Quaestiones Mathematicae 37(2014), 401-414