Some properties of the nilradical and non-nilradical graphs over finite commutative ring \(\mathbb{Z}_n\)
Let \(\mathbb{Z}_n\) be the finite commutative ring of residue classes modulo \(n\) with identity and \(\Gamma(\mathbb{Z}_n)\) be its zero-divisor graph. In this paper, we investigated some properties of nilradical graph, denoted by \(N(\mathbb{Z}_n)\) and non-nilradical graph, denoted by \(\Omega(\...
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| Datum: | 2018 |
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| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/54 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543432113127424 |
|---|---|
| author | Chandra, Shalini Prakash, Om Suthar, Sheela |
| author_facet | Chandra, Shalini Prakash, Om Suthar, Sheela |
| author_sort | Chandra, Shalini |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T02:43:18Z |
| description | Let \(\mathbb{Z}_n\) be the finite commutative ring of residue classes modulo \(n\) with identity and \(\Gamma(\mathbb{Z}_n)\) be its zero-divisor graph. In this paper, we investigated some properties of nilradical graph, denoted by \(N(\mathbb{Z}_n)\) and non-nilradical graph, denoted by \(\Omega(\mathbb{Z}_n)\) of \(\Gamma(\mathbb{Z}_n)\). In particular, we determined the Chromatic number and Energy of \(N(\mathbb{Z}_n)\) and \(\Omega(\mathbb{Z}_n)\) for a positive integer \(n\). In addition, we have found the conditions in which \(N(\mathbb{Z}_n)\) and \(\Omega(\mathbb{Z}_n)\) graphs are planar. We have also given MATLAB coding of our calculations. |
| first_indexed | 2026-02-08T07:59:33Z |
| format | Article |
| id | admjournalluguniveduua-article-54 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:59:33Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-542018-04-26T02:43:18Z Some properties of the nilradical and non-nilradical graphs over finite commutative ring \(\mathbb{Z}_n\) Chandra, Shalini Prakash, Om Suthar, Sheela commutative ring, zero-divisor graph, nilradical graph, non-nilradical graph, chromatic number, planar graph, energy of a graph 13A10, 05C10, 05C15, 05C25 Let \(\mathbb{Z}_n\) be the finite commutative ring of residue classes modulo \(n\) with identity and \(\Gamma(\mathbb{Z}_n)\) be its zero-divisor graph. In this paper, we investigated some properties of nilradical graph, denoted by \(N(\mathbb{Z}_n)\) and non-nilradical graph, denoted by \(\Omega(\mathbb{Z}_n)\) of \(\Gamma(\mathbb{Z}_n)\). In particular, we determined the Chromatic number and Energy of \(N(\mathbb{Z}_n)\) and \(\Omega(\mathbb{Z}_n)\) for a positive integer \(n\). In addition, we have found the conditions in which \(N(\mathbb{Z}_n)\) and \(\Omega(\mathbb{Z}_n)\) graphs are planar. We have also given MATLAB coding of our calculations. Lugansk National Taras Shevchenko University Indian Institute of Technology Patna 2018-01-24 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/54 Algebra and Discrete Mathematics; Vol 24, No 2 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/54/pdf Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | commutative ring zero-divisor graph nilradical graph non-nilradical graph chromatic number planar graph energy of a graph 13A10 05C10 05C15 05C25 Chandra, Shalini Prakash, Om Suthar, Sheela Some properties of the nilradical and non-nilradical graphs over finite commutative ring \(\mathbb{Z}_n\) |
| title | Some properties of the nilradical and non-nilradical graphs over finite commutative ring \(\mathbb{Z}_n\) |
| title_full | Some properties of the nilradical and non-nilradical graphs over finite commutative ring \(\mathbb{Z}_n\) |
| title_fullStr | Some properties of the nilradical and non-nilradical graphs over finite commutative ring \(\mathbb{Z}_n\) |
| title_full_unstemmed | Some properties of the nilradical and non-nilradical graphs over finite commutative ring \(\mathbb{Z}_n\) |
| title_short | Some properties of the nilradical and non-nilradical graphs over finite commutative ring \(\mathbb{Z}_n\) |
| title_sort | some properties of the nilradical and non-nilradical graphs over finite commutative ring \(\mathbb{z}_n\) |
| topic | commutative ring zero-divisor graph nilradical graph non-nilradical graph chromatic number planar graph energy of a graph 13A10 05C10 05C15 05C25 |
| topic_facet | commutative ring zero-divisor graph nilradical graph non-nilradical graph chromatic number planar graph energy of a graph 13A10 05C10 05C15 05C25 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/54 |
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