A graph Gamma is said to be End-regular if its endomorphism monoid End(Gamma) is regular. D. Lu and T. Wu 25 posed an open problem: Given a ring R, when does the zero-divisor graph Gamma (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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