Randić spectrum of the weakly zero-divisor graph of the ring ℤn
In this article, we find the Randić spectrum of the weakly zero-divisor graph of a finite commutative ring [Formula: see text] with identity [Formula: see text], denoted as [Formula: see text], where [Formula: see text] is taken as the ring of integers modulo [Formula: see text]. The weakly zero-div...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2024.2358360 |
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| author | Nadeem Ur Rehman Nazim Ahmad M. Alghamdi Eman S. Almotairi |
| author_facet | Nadeem Ur Rehman Nazim Ahmad M. Alghamdi Eman S. Almotairi |
| author_sort | Nadeem Ur Rehman |
| collection | DOAJ |
| description | In this article, we find the Randić spectrum of the weakly zero-divisor graph of a finite commutative ring [Formula: see text] with identity [Formula: see text], denoted as [Formula: see text], where [Formula: see text] is taken as the ring of integers modulo [Formula: see text]. The weakly zero-divisor graph of the ring [Formula: see text] is a simple undirected graph with vertices representing non-zero zero-divisors in [Formula: see text]. Two vertices, denoted as a and b, are connected if there are elements x in the annihilator of a and y in the annihilator of b such that their product xy equals zero. In particular, we examine the Randić spectrum of [Formula: see text] for specific values of [Formula: see text], which are products of prime numbers and their powers. |
| format | Article |
| id | doaj-art-73f42b2bf66e4bd18889a67e51e8ceb5 |
| institution | Kabale University |
| issn | 0972-8600 2543-3474 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj-art-73f42b2bf66e4bd18889a67e51e8ceb52024-12-05T07:02:08ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742024-09-0121330230910.1080/09728600.2024.2358360Randić spectrum of the weakly zero-divisor graph of the ring ℤnNadeem Ur Rehman0Nazim1Ahmad M. Alghamdi2Eman S. Almotairi3Department of Mathematics, Aligarh Muslim University, Aligarh, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaMathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah, Saudi ArabiaMathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah, Saudi ArabiaIn this article, we find the Randić spectrum of the weakly zero-divisor graph of a finite commutative ring [Formula: see text] with identity [Formula: see text], denoted as [Formula: see text], where [Formula: see text] is taken as the ring of integers modulo [Formula: see text]. The weakly zero-divisor graph of the ring [Formula: see text] is a simple undirected graph with vertices representing non-zero zero-divisors in [Formula: see text]. Two vertices, denoted as a and b, are connected if there are elements x in the annihilator of a and y in the annihilator of b such that their product xy equals zero. In particular, we examine the Randić spectrum of [Formula: see text] for specific values of [Formula: see text], which are products of prime numbers and their powers.https://www.tandfonline.com/doi/10.1080/09728600.2024.2358360Weakly zero-divisor graphRandić spectrumEuler totient functionring of integers modulo05C2505C50 |
| spellingShingle | Nadeem Ur Rehman Nazim Ahmad M. Alghamdi Eman S. Almotairi Randić spectrum of the weakly zero-divisor graph of the ring ℤn AKCE International Journal of Graphs and Combinatorics Weakly zero-divisor graph Randić spectrum Euler totient function ring of integers modulo 05C25 05C50 |
| title | Randić spectrum of the weakly zero-divisor graph of the ring ℤn |
| title_full | Randić spectrum of the weakly zero-divisor graph of the ring ℤn |
| title_fullStr | Randić spectrum of the weakly zero-divisor graph of the ring ℤn |
| title_full_unstemmed | Randić spectrum of the weakly zero-divisor graph of the ring ℤn |
| title_short | Randić spectrum of the weakly zero-divisor graph of the ring ℤn |
| title_sort | randic spectrum of the weakly zero divisor graph of the ring zn |
| topic | Weakly zero-divisor graph Randić spectrum Euler totient function ring of integers modulo 05C25 05C50 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2024.2358360 |
| work_keys_str_mv | AT nadeemurrehman randicspectrumoftheweaklyzerodivisorgraphoftheringzn AT nazim randicspectrumoftheweaklyzerodivisorgraphoftheringzn AT ahmadmalghamdi randicspectrumoftheweaklyzerodivisorgraphoftheringzn AT emansalmotairi randicspectrumoftheweaklyzerodivisorgraphoftheringzn |