INVERSE DOMINATION AND INVERSE TOTAL DOMINATION FOR AN UNDIRECTED GRAPH

Abstract

In this paper we analyze the domination parameters such as inverse domination and inverse total domination number of an undirected graph G_(m,n) and obtained several results on these parameters. An undirected graph G_(m,n) is a graph defined in [1],whose vertex set V=I_n={1,2,3,…..n} and r,s?V are adjacent if and only if r?s and r+s†m, where m,n?N and m>1. A set D of vertices of a graph G is a dominating set if every vertex in V-D is adjacent to some vertex in D. Let D be a minimum dominating set of G. If V-D contains a dominating set sayD^' of G, then D^' is called an inverse dominating set with respect to D.In this paper we obtain exact values of ??^(-1) (G?_(m,n)) for different values of m,n.