The adjacency matrix of the conjugate graph of metacyclic 2-groups

Abstract

Let G be a metacyclic 2-group and gamma(conj,G) is the conjugate graph of G. The vertices of gamma(conj,G) are non-central elements in which two vertices are adjacent if they are conjugate. The adjacency matrix of gamma(conj,G) is a matrix A=[a(i,j)] consisting 0's and 1's in which the entry a(i,j) is 1 if there is an edge between ith and jth vertices and 0 otherwise. In this paper, the adjacency matrix of a conjugate graph of metacyclic 2-groups is presented.