On Domination in Zero-divisor graphs of rings with involution
Bull. Korean Math. Soc.
Published online June 29, 2021
Mohd Nazim, Junaid Nisar, and Nadeem ur Rehman
Aligarh Muslim University; Aligarh Muslim University; Aligarh Muslim University
Abstract : In this article, we discuss the domination in the zero-divisor graph of a $\ast$-ring. We first determine the domination number, the total domination number, and the connected domination number for the zero-divisor graph of the product of two $\ast$-rings with componentwise involution. Then, we study domination in the zero-divisor graph of a Rickart $\ast$-ring and relate it with the clique of the zero-divisor graph of a Rickart $\ast$-ring.
Keywords : $\ast$-ring, Rickart $\ast$-ring, Domination number, Dominating set, Zero-divisor graph.
MSC numbers : 16W10, 05C69, 05C25
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