On the metric dimension of extended zero divisor graphs

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S. Nithya
V. Prisci

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 xmym=0 with xm0 and yn0. 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.

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How to Cite
Nithya, S., & Prisci, V. (2024). On the metric dimension of extended zero divisor graphs. Gulf Journal of Mathematics, 16(1), 205-214. https://doi.org/10.56947/gjom.v16i1.1801
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