• CONNECTED ENTIRE DOMINATION IN GRAPHS

Abstract

The vertices and edges of a graph G are called the elements of G. A set X of elements in G is an entire dominating set if every element not in X is an entire dominating set if every element not in X is either adjacent or incident to at least one element in X. An entire dominating set X of G is a connected entire dominating set if the induced subgraph áXñ is connected. The connected entire domination number e_c(G) of G is the minimum cardinality of a connected entire dominating set in G. In this paper, we initiate a study of this parameter and present some bounds and some exact values for e_c(G). Also Nordhaus Gaddum type results are obtained.