Maximal Graph of a Commutative Ring
نویسندگان
چکیده
Abstract Let R be a commutative ring with identity. Let G be a graph with vertices as elements of R, where two distinct vertices a and b are adjacent if and only if there is a maximal ideal of R containing both. In this paper we show that a ring R is finite if and only if clique number of the graph G (associated with R as above) is finite. We also have shown that for a semilocal ring R, the chromatic number of the graph G is equals to the clique number of G which turns out to be the maximum of the cardinalities of all the maximal ideals in R.
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