CONNECTED VERTEX-EDGE DOMINATION POLYNOMIALS OF SOME GRAPHS
In this paper, we introduce the concept of connected vertex-edge domination polynomial for any graph G. The connected vertex-edge domination polynomial of a graph G of order n is the polynomial where is the number of connected vertex-edge dominating sets of G of size i and is the connected vertex-edge domination number of G. We obtain some properties of and its coefficients. Also, we calculate the connected vertex-edge domination polynomials for the complete graph the star graph the Barbell graph and the Tadpole graph
connected vertex-edge dominating sets, connected vertex-edge domination number, connected vertex-edge domination polynomial.