FAULT-TOLERANT METRIC DIMENSION OF ANNIHILATOR GRAPHS OF COMMUTATIVE RINGS

Abstract

Let R be a commutative ring with identity. The annihilator graph AG (R) is a simple graph with vertex set as the set of all non-zero zero-divisors of R, and two distinct vertices a and b are adjacent if and only if annR (a) ∪ annR (b) ̸= annR (a · b). We depicted the relationship between the fault-tolerant metric dimension of AG (R) and some graph parameters. Furthermore, we computed the fault-tolerant metric dimension of the annihilator graph of reduced and non-reduced rings.