Abstract

. Given a graph , comprising a set of vertices and a set of edges. A set is a dominating set of , if every vertex in is adjacent to at least one vertex in . The cardinality of minimum dominating set of it's domination number and is denoted by . A set is a eccentric dominating set if is an dominating set of and for every in there exist at least one eccentric point of in . The cardinality of minimum eccentric dominating set of it's eccentric domination number and is denoted by . A set is a connected eccentric dominating set if is an eccentric dominating set of and the induced subgraph is connected. The cardinality of minimum connected eccentric dominating set of it's connected eccentric domination number and is denoted by . In this paper we discuss connected eccentric dominating set and connected eccentric domination number on special graphs which are complete graph, star graph, complete bipartite graph, cycel graph and wheel graph.