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.

MSC: 05C99, 13A15, 13F10

Received: 29.09.2015
Revised: 19.10.2017

Language: English

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