Domination polynomial and total domination polynomial of zero-divisor graphs of commutative rings
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914763856936960 |
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| author | Alikhani, Saeid Aghaei, Fatemeh |
| author_facet | Alikhani, Saeid Aghaei, Fatemeh |
| contents | 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 $ \mathbb{Z}_n $ where $ n\in\lbrace 2p, p^2, pq, p^2q, pqr, p^α\rbrace $, and $ p, q, r $ are primes with $ p>q>r>2 $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13539 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Domination polynomial and total domination polynomial of zero-divisor graphs of commutative rings Alikhani, Saeid Aghaei, Fatemeh Combinatorics 05C69, 05C25 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 $ \mathbb{Z}_n $ where $ n\in\lbrace 2p, p^2, pq, p^2q, pqr, p^α\rbrace $, and $ p, q, r $ are primes with $ p>q>r>2 $. |
| title | Domination polynomial and total domination polynomial of zero-divisor graphs of commutative rings |
| topic | Combinatorics 05C69, 05C25 |
| url | https://arxiv.org/abs/2404.13539 |