$Some properties of the nilradical and non-nilradical graphs over finite commutative ring $\mathbb{Z}_n$$

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(\...

Full description

Saved in:

Bibliographic Details
Date:	2018
Main Authors:	Chandra, Shalini, Prakash, Om, Suthar, Sheela
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2018
Subjects:	commutative ring zero-divisor graph nilradical graph non-nilradical graph chromatic number planar graph energy of a graph 13A10 05C10 05C15 05C25
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/54
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Algebra and Discrete Mathematics

Institution

Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-54
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua: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
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-04-26T02:43:18Z
collection	OJS
language	English
topic	commutative ring zero-divisor graph nilradical graph non-nilradical graph chromatic number planar graph energy of a graph 13A10 05C10 05C15 05C25
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 $\mathbb{Z}_n$
topic_facet	commutative ring zero-divisor graph nilradical graph non-nilradical graph chromatic number planar graph energy of a graph 13A10 05C10 05C15 05C25
format	Article
author	Chandra, Shalini Prakash, Om Suthar, Sheela
author_facet	Chandra, Shalini Prakash, Om Suthar, Sheela
author_sort	Chandra, Shalini
title	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_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_sort	some properties of the nilradical and non-nilradical graphs over finite commutative ring $\mathbb{z}_n$
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.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/54
work_keys_str_mv	AT chandrashalini somepropertiesofthenilradicalandnonnilradicalgraphsoverfinitecommutativeringmathbbzn AT prakashom somepropertiesofthenilradicalandnonnilradicalgraphsoverfinitecommutativeringmathbbzn AT sutharsheela somepropertiesofthenilradicalandnonnilradicalgraphsoverfinitecommutativeringmathbbzn
first_indexed	2025-07-17T10:33:44Z
last_indexed	2025-07-17T10:33:44Z
_version_	1837889982439620608

Some properties of the nilradical and non-nilradical graphs over finite commutative ring \(\mathbb{Z}_n\)

Institution

Similar Items