Domination polynomial and total domination polynomial of zero-divisor graphs of commutative rings

The domination polynomial (the total domination polynomial) of a graph G of order n is the generating function of the number of dominating sets (total dominating sets) of G of any size. In this paper, we study the domination polynomial and the total domination polynomial of zero-divisor graphs of the ring Zₙ where n∈ 2p, p², pq, p²q, pqr, p^α, and $ p, q, r $ are primes with $ p>q>r>2 $.