Vertex- Edge Dominating Sets and Vertex-Edge Domination Polynomials of Wheels

Abstract

Let G = (V, E) be a simple Graph. A set S  V(G) is a vertex-edge dominating set (or simply ve-dominating set) if for all edges e  E(G), there exist a vertex v  S such that v dominates e. In this paper, we study the concept of vertex-edge domination polynomial of the cycle Cn. The vertex-edge domination polynomial of Cn is Dve(Cn, x) = |V(G)|