End-regularity of zero-divisor graphs of group rings |
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| Authors: | Dengyin Wang Xiaobin Ma Chunguang Xia |
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| Institution: | 1. Department of Mathematics, China University of Mining and Technology, Xuzhou, P. R. Chinawdengyin@126.com;3. Department of Mathematics, China University of Mining and Technology, Xuzhou, P. R. China |
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| Abstract: | A graph Γ is said to be End-regular if its endomorphism monoid End(Γ) is regular. D. Lu and T. Wu 25 Lu, D., Wu, T. (2008). On endomorphism-regularity of zero-divisor graphs. Discrete Math. 308:4811–4815.Crossref], Web of Science ®] , Google Scholar]] posed an open problem: Given a ring R, when does the zero-divisor graph Γ(R) have a regular endomorphism monoid? and they solved the problem for R a commutative ring with at least one nontrivial idempotent. In this paper, we solve this problem for zero-divisor graphs of group rings. |
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| Keywords: | End-regular graphs group rings zero-divisor graphs |
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