Covering matrices of a graph

Abstract

Given a Graph G = ((V(G),E(G)), and a subset , S with a given property(covering set, Dominating set, Neighbourhood set), we define a matrix taking a row for each of the minimal set corresponding to the given property and a column for each of the vertex of G. The elements of the matrix are 1 or 0 respectively as the vertex is contained in minimal set or otherwise. That is matrix (mij) has elements mij and

mij = 1 if ith row minimal set contains jth vertex = 0 otherwise

This paper initiates a study on these new types of matrices of a graph and we characterize such matrices for some special classes of graphs.