Fault-Tolerant Metric Dimension of Annihilator Graphs of Commutative Rings

Document Type : Original Manuscript

Authors

1 Department of Mathematics, University College, University of Kerala, Thiruvananthapuram, kerala,India

2 Professor, Department of Mathematics, University College, University of Kerala,Thiruvananthapuram, Kerala, India

10.22044/jas.2023.12666.1690

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.

Keywords

Journal of Algebraic Systems

Articles in Press, Accepted Manuscript
Available Online from 09 April 2024

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