Shahrood University of TechnologyJournal of Algebraic Systems2345-5128Articles in Press20240409FAULT-TOLERANT METRIC DIMENSION OF ANNIHILATOR GRAPHS OF COMMUTATIVE RINGS310310.22044/jas.2023.12666.1690ENMohan S. AkhilaDepartment of Mathematics, University College, University of Kerala, Thiruvananthapuram, India.0000-0003-0889-1525Karunakaran ManilalDepartment of Mathematics, University College, University of Kerala, Thiruvananthapuram, India.Journal Article20230223Let 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.https://jas.shahroodut.ac.ir/article_3103_70aa6354b888a9a0615d51314c82f5ce.pdf