• VERTEX- EDGE DOMINATION POLYNOMIALS OF GRAPHS

Abstract

In this paper, we introduce the concept of vertex-edge domination polynomial for any Graph. The vertex-edge domination polynomial of a graph G of order n is the polynomia D_ve (G, x) = where  d_ve(G, i) is the number of vertex-edge dominating sets of G of size i, and g_ve(G) is the vertex-edge domination number of G. We obtain some properties of D_ve(G, x) and its co-efficients. Also, we find the vertex-edge domination polynomial for the complete Graph K_n, G o K₁ and G o K₂ .