  We introduce a new bivariate polynomial ${\displaystyle J(G;
x,y):=\sum\limits_{W \in V(G)} x^{|W|}y^{|N(W)|}}$ which contains the standard
domination polynomial of the graph $G$ in two different ways. We build methods
for efficient calculation of this polynomial and prove that there are still
some families of graphs which have the same bivariate polynomial.
