Connected Equitable Domination in Graphs
S. Sivakumar, N. D. Soner, Anwar Alwardi, G. Deepak · MyPrints@UOM (Mysore University Library) · 2012
Let G = (V,E) be a graph. A subset D of V is called an equitable dominating set of a graph G if for every v . V -D, there exists a vertex v . D such that uv . E(G) and |deg(u) - deg(v)| = 1, where deg(u) is the degree of u and deg(v) is the degree of v in G. An equitable dominating set D is said to be a connected equitable dominating set if the subgraph �D� induced by D is connected. The minimum of the cardinalities of the connected equitable dominating sets of G is called the connected equitable domination number and denoted by .ce(G) In this paper we introduce the connected equitable domination and connected equitable domatic in a graph, bounds for .ce(G), dce(G) and its exact values for some standard graphs are found.