• 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 sdgle(G). In this paper, we establish bounds on the locating equitable domination subdivision number for some families of graphs.
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