2-domination polynomials of graphs

Abstract

Let G be a simple graph of order m. Let D2(G, i) be the family of 2-dominating sets in G with size i. The polynomial D2(G, ) = is called the 2-domination polynomial of G. Let D2(Sm, i) be the family of 2-dominating sets of the spider graph Sm with cardinality i and let d2(Sm, i) = |D2(Sm, i)|. Then the 2-domination polynomial D2(Sm, ) of Sm is defined as D2(Sm, ) = , where is the 2-domination number of Sm. In this paper, we obtain some operations on graphs.