Minimum second neighborhood degree energy of commuting graphs of finite rings
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913152170459136 |
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| author | Tak, Payal Dutta, Jutirekha Nath, Rajat Kanti |
| author_facet | Tak, Payal Dutta, Jutirekha Nath, Rajat Kanti |
| contents | In this paper, we compute minimum second neighborhood degree spectrum and energy of commuting graphs of certain finite non-commutative rings. In particular, we consider non-commutative rings of order $p^2, p^3, p^4, p^5, p^2q$ and $p^3q$, where $p$ and $q$ are primes. We shall also show that the commuting graphs of these rings are MSN-integral but not MSN-hyperintegral. Finally, employing the techniques used in this paper, we prove Conjecture 3 of [Nath, R. K., Fasfous, W. N. T., Das, K. C. and Shang, Y. Common neighbourhood energy of commuting graphs of finite groups, {\em Symmetry} {\bf 13}(9), Article No. 1651, 2021.] and Conjecture 3.12 of [W. N. T. Fasfous and Nath, R. K. Common neighborhood spectrum and energy of commuting graphs of finite rings, \emph{ Palestine J. Math.} \textbf{13}(1), 66--76, 2024.]. We conclude this paper with two open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22160 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimum second neighborhood degree energy of commuting graphs of finite rings Tak, Payal Dutta, Jutirekha Nath, Rajat Kanti Rings and Algebras In this paper, we compute minimum second neighborhood degree spectrum and energy of commuting graphs of certain finite non-commutative rings. In particular, we consider non-commutative rings of order $p^2, p^3, p^4, p^5, p^2q$ and $p^3q$, where $p$ and $q$ are primes. We shall also show that the commuting graphs of these rings are MSN-integral but not MSN-hyperintegral. Finally, employing the techniques used in this paper, we prove Conjecture 3 of [Nath, R. K., Fasfous, W. N. T., Das, K. C. and Shang, Y. Common neighbourhood energy of commuting graphs of finite groups, {\em Symmetry} {\bf 13}(9), Article No. 1651, 2021.] and Conjecture 3.12 of [W. N. T. Fasfous and Nath, R. K. Common neighborhood spectrum and energy of commuting graphs of finite rings, \emph{ Palestine J. Math.} \textbf{13}(1), 66--76, 2024.]. We conclude this paper with two open problems. |
| title | Minimum second neighborhood degree energy of commuting graphs of finite rings |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2605.22160 |