INVERSE AND DISJOINT SECURE DOMINATING SETS IN GRAPHS

Abstract

Let D be a minimum secure dominating set of a graph G = (V, E). If V – D contains a secure dominating set D' of G, then D' is called an inverse secure dominating set with respect to D. The inverse secure domination number g_s^-1(G) of G is the minimum cardinality of an inverse secure dominating set of G. The disjoint secure domination number g_sg_s(G) of a graph G is the minimum cardinality of the union of two disjoint secure dominating sets in G. In this paper, we establish some results for the inverse secure domination number. Also we initiate a study of the disjoint secure domination number and obtain some results on this new parameter.