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 is an element of V are adjacent if and only if r not equal s and r + s dagger m, where m, n is an element of N and in > 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 say D' of G, then D' is called an inverse dominating set with respect to D. In this paper we obtain exact values of gamma(-1) (G(m, n)) and gamma(-1)(t) (G(m, n)) for different values of m, n.