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Algebra and Discrete Mathematics, 2017, Volume 24, Issue 2, Pages 250–261
(Mi adm631)
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RESEARCH ARTICLE
The edge chromatic number of $\Gamma_{I}(R)$
R. Kala, A. Mallika, K. Selvakumar Department of Mathematics, Manonmaniam Sundaranar University,
Tirunelveli 627 012, Tamil Nadu, India
Abstract:
For a commutative ring $R$ and an ideal $I$ of $R$, the ideal-based zero-divisor graph is the undirected graph $\Gamma_{I}(R)$ with vertices $\{x\in R-I\colon xy\in I \text{ for some } y\in R-I\}$, where distinct vertices $x$ and $y$ are adjacent if and only if $xy\in I$. In this paper, we discuss the nature of the edges of $\Gamma_{I}(R)$. We also find the edge chromatic number for the graph $\Gamma_{I}(R)$.
Keywords:
zero-divisor graph, chromatic number, ideal-based zero-divisor graph.
Received: 29.09.2015 Revised: 19.10.2017
Citation:
R. Kala, A. Mallika, K. Selvakumar, “The edge chromatic number of $\Gamma_{I}(R)$”, Algebra Discrete Math., 24:2 (2017), 250–261
Linking options:
https://www.mathnet.ru/eng/adm631 https://www.mathnet.ru/eng/adm/v24/i2/p250
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Abstract page: | 120 | Full-text PDF : | 96 | References: | 25 |
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