• BOUNDS ON LOCATING EQUITABLE DOMINATION SUBDIVISION NUMBERS OF GRAPHS

Abstract

Let G = (V, E) be a simple, undirected, finite nontrivial graph. A non empty set DÍ V of vertices in a graph G is a dominating set if every vertex in V-D is adjacent to some vertex in   D. The domination number g(G) is the minimum cardinality of a dominating set of G. A dominating set D is  a  locating equitable dominating set of G if for any two vertices u,wÎV-D, N(u)ÇD ¹ N(w)ÇD, ½N(u)ÇD½=½N(w)ÇD½. The locating equitable domination number of G is the minimum cardinality of a locating equitable dominating set of G. The locating equitable domination subdivision number of G is the minimum number of edges that must be subdivided(where each edge in G can be subdivided at most once) in order to increase the locating equitable domination number and is denoted by sdg_le(G). In this paper, we establish bounds on the locating equitable domination subdivision number for some families of graphs.