On the metric dimension of extended zero divisor graphs

Abstract

Let R be a commutative ring with unity, the extended zero divisor graph E(R) is defined by considering the non-zero zero divisors Z(R)^∗ as the vertices and two distinct vertices x and y of R are adjacent whenever there exist two positive integers m and n such that x^my^m=0 with x^m≠0 and yⁿ≠ 0. In this paper, we investigate metric dimension, fault tolerant metric dimension and local metric dimension of the extended zero divisor graph for the ring of integers modulo m and the ring of Gaussian integers modulo m.