Connected Equitable Domination in Graphs

Abstract

Abstract 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 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 γ ce (G) In this paper we introduce the connected equitable domination and connected equitable domatic in a graph, bounds for γ ce (G), d ce (G) and its exact values for some standard graphs are found. Mathematics Subject Classification: 05C6