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- Title
CO-MAXIMAL IDEAL GRAPHS OF COMMUTATIVE RINGS.
- Authors
YE, MENG; WU, TONGSUO
- Abstract
In this paper, a new kind of graph on a commutative ring R with identity, namely the co-maximal ideal graph is defined and studied. We use to denote this graph, with its vertices the proper ideals of R which are not contained in the Jacobson radical of R, and two vertices I1 and I2 are adjacent if and only if I1 + I2 = R. We show some properties of this graph. For example, this graph is a simple, connected graph with diameter less than or equal to three, and both the clique number and the chromatic number of the graph are equal to the number of maximal ideals of the ring R.
- Subjects
MAXIMAL ideals; GRAPH theory; COMMUTATIVE rings; JACOBSON radical; NUMBER theory; DIAMETER
- Publication
Journal of Algebra & Its Applications, 2012, Vol 11, Issue 6, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498812501149