On the Domination Polynomial of Some Graph Operations

Abstract

Let G be a simple graph of order n . The domination polynomial of G is the polynomial D ( G , λ ) = ∑ i = 0 n ‍ d ( G , i ) λ i , where d ( G , i ) is the number of dominating sets of G of size i . Every root of D ( G , λ ) is called the domination root of G . In this paper, we study the domination polynomial of some graph operations.