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http://dx.doi.org/10.4134/BKMS.b200968

ON DOMINATION IN ZERO-DIVISOR GRAPHS OF RINGS WITH INVOLUTION  

Nazim, Mohd (Department of Mathematics Aligarh Muslim University)
Nisar, Junaid (Department of Mathematics Aligarh Muslim University)
Rehman, Nadeem ur (Department of Mathematics Aligarh Muslim University)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.6, 2021 , pp. 1409-1418 More about this Journal
Abstract
In this paper, we study domination in the zero-divisor graph of a *-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 *-rings with componentwise involution. Then, we study domination in the zero-divisor graph of a Rickart *-ring and relate it with the clique of the zero-divisor graph of a Rickart *-ring.
Keywords
*-ring; Rickart *-ring; domination number; dominating set; zero-divisor graph;
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