CO-MAXIMAL IDEAL GRAPHS OF COMMUTATIVE RINGS
CO-MAXIMAL IDEAL GRAPHS OF COMMUTATIVE RINGS
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DOI：
10.1142/s0219498812501149
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发表时间：
2012-11
影响因子：
0.8
通讯作者：
Meng Ye;Tongsuo Wu
中科院分区：
文献类型：
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作者：
Meng Ye;Tongsuo Wu
本文在具有单位元的交换环R上定义并研究了一类新的图，即余极大理想图。我们用$\mathscr{C}(R)$来表示这个图，它的顶点是不包含在R的Jacobson根中的R的真理想，并且两个顶点I1和I2是相邻的当且仅当I1+I2=R。例如，这个图是一个直径小于等于3的简单连通图，它的团数和色数都等于环R的极大理想数。
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 $\mathscr{C}(R)$ 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.