Table of Contents
ISRN Combinatorics
Volume 2013 (2013), Article ID 354696, 7 pages
http://dx.doi.org/10.1155/2013/354696
Research Article

On Graphs Related to Comaximal Ideals of a Commutative Ring

1Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
2Department of Mathematics, Soochow University, Suzhou, Jingsu 215006, China
3School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received 11 October 2012; Accepted 29 October 2012

Academic Editors: C. da Fonseca, R. Dondi, E. Kiliç, and S. Zhou

Copyright © 2013 Tongsuo Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the co maximal graph , the induced subgraph of whose vertex set is , and a retract of , where is a commutative ring. For a graph which contains a cycle, we show that the core of is a union of triangles and rectangles, while a vertex in is either an end vertex or a vertex in the core. For a nonlocal ring , we prove that both the chromatic number and clique number of are identical with the number of maximal ideals of . A graph is also introduced on the vertex set , and graph properties of are studied.