Connected Vertex-Edge Dominating Sets and Connected Vertex-Edge Domination Polynomials of Friendship F_n

Abstract

Let  be a simple connected graph of order  Let be the family of connected vertex-edge dominating sets in  with cardinality .The polynomial is called the connected vertex - edge domination polynomial of  G, where  is the number of connected vertex - edge dominating sets of G. In this paper, we study some properties of connected vertex-edge domination polynomials of the Friendship graph . We obtain a recursive formula for   . Using this recursive formula, we construct the connected vertex - edge domination polynomial  of , where  is the number of the connected vertex - edge dominating sets of  of cardinality  and some properties of this polynomial have been studied.