Connected domination value in graphs

In a connected graph G = (V, E), a set D subset of V is a connected dominating set if for every vertex V is an element of V \ D, there exists u is an element of D such that u and v are adjacent, and the subgraph < D > induced by D in G is connected. A connected dominating set of minimum cardinality is called a gamma(c)-set of G. For each vertex v is an element of V, we define the connected domination value of v to be the number of gamma(c)-sets of G to which v belongs. In this paper, we study the properties of connected domination value of a connected graph G and its relation to other parameters of a connected graph. Finally, we compute the connected domination value and number of gamma(c)-sets for a few well-known family of graphs.