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Commutative rings whose zero-divisor graph is a proper refinement of a star graph

✍ Scribed by Qiong Liu; Tong Suo Wu

Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2011
Tongue
English
Weight
256 KB
Volume
27
Category
Article
ISSN
1439-7617

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For each commutative ring R we associate a simple graph ⌫ R . We investigate the interplay between the ring-theoretic properties of R and the graph-theo-Ž . retic properties of ⌫ R .

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✍ S. Akbari; A. Mohammadian πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 192 KB

Let R be a commutative ring and Ξ“ (R) be its zero-divisor graph. In this paper it is shown that for any finite commutative ring R, the edge chromatic number of Ξ“ (R) is equal to the maximum degree of Ξ“ (R), unless Ξ“ (R) is a complete graph of odd order. In [D.F.