ANTIADJACENCY MATRICES FOR SOME STRONG PRODUCTS OF GRAPHS

Aluysius Sutjijana, Dea Alvionita Azka
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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.
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一些图的强积的反相邻矩阵
假设 G 是一个没有多条边的无向图。表示图的方法有很多,其中一种是矩阵形式,即构建反相接矩阵。给定一个连通图 G,其顶点集 $V$ 由 n 个成员组成,图 G 的反相接矩阵是一个 n 次的矩阵 B,如果有一条边连接顶点 v_i 和顶点 v_j(v_i \sim v_j ),则 B 的第 i^{th} 行和第 b^{th} 列的元素为 0,否则为 1。本文研究了两个图的某些强积的反相邻矩阵的一些性质。我们的结果是在 m, n\ge 3 时路径图 P_m 与 P_n 以及在 m \ge 3 时循环图 C_m 与 C_m 的强积的反相邻矩阵的一般形式。
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