Let G be a simple graph of order n. The hop domination polynomial of G is the polynomial | ( )| ( ) ( , ) ( , ) , h V G i h i G h d G i d G i x =γ = Σ where dh(G, i) is the number of hop dominating sets of G of size i and gh(G) is the hop domination number of G. In this paper we study dh(G, i) of a graph. We classify many families of graphs by studying their hop domination polynomial.
