The main objective of this paper is to calculate the metric dimension and resolving-domination number of zero-divisor graphs of direct product of finite fields. Let   be finite fields. We consider the zero-divisor graph  of the ring  of direct product of finite fields. We determine metric dimension  and resolving-domination number  of the ring of direct product of finite fields. If the order of each  field is two, then we prove that the metric dimension  and resolving-domination number  If the order of each field is at least 3, then we prove that the metric dimension  and resolving-domination number  are both equal to

zero-divisor graphs, metric dimension, resolving domination number.

Received: February 19, 2023; Revised: July 1, 2023; Accepted: July 4, 2023

How to cite this article: Subhash Mallinath Gaded and Nithya Sai Narayana, On metric dimension and resolving-domination number of zero-divisor graphs of direct product of finite fields, JP Journal of Algebra, Number Theory and Applications 61(2) (2023), 171-182.
http://dx.doi.org/10.17654/0972555523016

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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