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37 - M. Behboodi (with Gh. Aalipour, S. Akbari, R. Nikandish, M.J. Nikmehr, F. Shaveisi), The classification of the annihilating- ideal graph of a commutative ring. Algebra Colloquium 21(2) (2014), 249-256. (ISI)

Let R be a commutative ring and A(R) be the set of ideals with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)*=A(R)\{(0)} and two distinct vertices I and J are adjacent if and only if IJ = (0). Here, we present some results on the clique number and the chromatic number of the annihilating-ideal graph of a commutative ring. It is shown that if R is an Artinian ring and w(AG(R))=2, then R is Gorenstein. Also, we investigate commutative rings whose annihilating-ideal graph is complete or bipartite.



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