Abstract
The idempotent graph I(R) of a ring R is a graph with nontrivial idempotents of R as vertices, and two vertices are adjacent in I(R) if and only if their product is zero. In the present paper, we prove that idempotent graphs are weakly perfect. We characterize the rings whose idempotent graphs have connected complements. As an application, the idempotent graph of an abelian Rickart ring R is used to obtain the zero-divisor graph \(\Gamma (R)\) of R.
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The authors express their deep gratitudes to the anonymous referee for many corrections in several revisions.
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Patil, A., Momale, P.S. Idempotent graphs, weak perfectness, and zero-divisor graphs. Soft Comput 25, 10083–10088 (2021). https://doi.org/10.1007/s00500-021-05982-0
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DOI: https://doi.org/10.1007/s00500-021-05982-0