Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2021; 58(6): 1409-1418

Published online November 30, 2021 https://doi.org/10.4134/BKMS.b200968

Copyright © The Korean Mathematical Society.

On domination in zero-divisor graphs of rings with involution

Mohd Nazim, Junaid Nisar, Nadeem ur Rehman

Aligarh Muslim University; Aligarh Muslim University; Aligarh Muslim University

Abstract

In this paper, we study 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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