Geodesic
The edge chromatic number of $\Gamma_{I}(R)$
Algebra and discrete mathematics, Tome 24 (2017) no. 2, pp. 250-261

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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. 
@article{ADM_2017_24_2_a5,
     author = {R. Kala and A. Mallika and K. Selvakumar},
     title = {The edge chromatic number of $\Gamma_{I}(R)$},
     journal = {Algebra and discrete mathematics},
     pages = {250--261},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2017_24_2_a5/}
}
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R. Kala; A. Mallika; K. Selvakumar. The edge chromatic number of $\Gamma_{I}(R)$. Algebra and discrete mathematics, Tome 24 (2017) no. 2, pp. 250-261. http://geodesic.mathdoc.fr/item/ADM_2017_24_2_a5/