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

2024/04/21 by Alikhani, Saeid, Aghaei, Fatemeh
#05C25 #05C69 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.13539

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 ℤ_n where n∈\lbrace 2p, p², pq, p²q, pqr, p^α\rbrace , and p, q, r are primes with p>q>r>2 .

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• On Domination in Zero-Divisor Graphs
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• Some new results on the total domination polynomial of a graph