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Abstract
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Let R be a commutative ring with unity. The comaximal ideal graph of R, denoted by
C(R), is a graph whose vertices are 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. In this paper, we
classify all comaximal ideal graphs with finite independence number and present a formula to calculate
this number. Also, the domination number of C(R) for a ring R is determined. In the last section,
we introduce all planar and toroidal comaximal ideal graphs. Moreover, the commutative rings with
isomorphic comaximal ideal graphs are characterized. In particular we show that every finite comaximal
ideal graph is isomorphic to some C(Zn
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