Let d_G(k) be the number of dominating sets of size k in a graph G, then the domination polynomial D_G(x) of G in the variable x is defined as D_G(x) = sum_(k = γ(G))^( left bracketing bar V(G) right bracketing bar ) d_G(k) x^k, where γ(G) is the (lower) domination number of G (Kotek et al. 2012, Alikhani and Peng 2014). D_G(x) is multiplicative over connected components. Nonisomorphic graphs may have the same domination polynomial. Graphs are said to be dominating equivalent if they have equal domination polynomials, and a graph that does not share a domination polynomial with any other nonisomorphic graph is said to be dominating unique .

domatic number | domatic partition | dominating set | domination number | upper domination number