CONNECTED SUPER DOMINATION IN GRAPHS

Let G be a simple graph. A set S subset of V(G) is a connected super dominating set if for every v is an element of V(G)\S, there exists an external private neighbor of v with respect to S and the subgraph < S > induced by S is connected. The connected super domination number of G, denoted by gamma(csp) (G), is the minimum cardinality of a connected super dominating set in G. A connected super dominating set S of G with vertical bar S vertical bar = gamma(csp)(G) is called a gamma(csp)-set of G. In this paper, the connected super dominating sets of some common graphs and the graphs resulting from the join, corona, lexicographic product and Cartesian product of graphs are characterized. Also, the connected super domination numbers of these graphs are determined.