ANTIADJACENCY MATRICES FOR SOME STRONG PRODUCTS OF GRAPHS

Abstract

Let G be an undirected graphs with no multiple edges. There are many ways to represent a graph, and one of them is in a matrix form, by constructing an antiadjacency matrix. Given a connected graph G with vertex set $V$ consisting of n members, an antiadjacency matrix of the graph G is a matrix B of order n \times n such that if there is an edge that connects vertex v_i to vertex v_j (v_i \sim v_j ) then the element of i^{th} row and b^{th} column of B is 0, otherwise 1. In this paper we investigate some properties of antiadjacency matrices for some strong product of two graphs. Our results are general forms of the antiadjacency matrix of the strong product of path graphs P_m with P_n for m, n\ge 3, and cycle graphs C_m with C_m for m \ge 3.