Domination Polynomial of the Composition of Complete Graph and Star Graph

Abstract

Abstract Graph domination by vertices is finding a subset D from the vertex set V(G), “in a graph G such that D is a dominating set if every vertex in set V – D is adjacent to at least one vertex in set D”, In this paper, D(G,i) when G is a composition of complete graph Kr and star graph S m , is constructed where “D(G,i), is the family of all dominating sets of a graph G with cardinality i and d(G,i) = |D(G, i)|”. A recursive formula for d(K r[Sm ], i) is obtained. The domination polynomial of graph K r[Sm ] is determined by using this recursive formula.