April 21, 2024Open Access

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

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Abstract

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.

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Alikhani et al. (Sun,) studied this question.

synapsesocial.com/papers/68e6e3f4b6db64358765fc38 https://doi.org/https://doi.org/10.48550/arxiv.2404.13539

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