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Algebra and Discrete Mathematics, 2017, том 24, выпуск 2, страницы 181–190
(Mi adm626)
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RESEARCH ARTICLE
Some properties of the nilradical and non-nilradical graphs over finite commutative ring $\mathbb{Z}_n$
Shalini Chandraa, Om Prakashb, Sheela Suthara a Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali, Rajasthan 304022, India
b Department of Mathematics, IIT Patna, Patliputra colony, Patna 800013, India
Аннотация:
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 investigate 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 determine 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.
Ключевые слова:
commutative ring, zero-divisor graph, nilradical graph, non-nilradical graph, chromatic number, planar graph, energy of a graph.
Поступила в редакцию: 24.09.2015 Исправленный вариант: 25.02.2016
Образец цитирования:
Shalini Chandra, Om Prakash, Sheela Suthar, “Some properties of the nilradical and non-nilradical graphs over finite commutative ring $\mathbb{Z}_n$”, Algebra Discrete Math., 24:2 (2017), 181–190
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm626 https://www.mathnet.ru/rus/adm/v24/i2/p181
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