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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^, and p, q, r are primes with p>q>r>2.
Alikhani et al. (Sun,) studied this question.