Fault-Tolerant Metric Dimension and Applications: Zero-Divisor Graph of Upper Triangular Matrices

Latif Abdelmalek Hanna (), Maryam M. Alkandari and Vijay Kumar Bhat
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Latif Abdelmalek Hanna: Department of Mathematics, Kuwait University, Kuwait City 13060, Kuwait
Maryam M. Alkandari: Department of Mathematics, Kuwait University, Kuwait City 13060, Kuwait
Vijay Kumar Bhat: School of Mathematics, Shri Mata Vaishno Devi University, Katra 182320, Jammu and Kashmir, India

Mathematics, 2025, vol. 13, issue 22, 1-12

Abstract: Graph invariants play a crucial role in understanding the structural and combinatorial characteristics of graphs. The fault-tolerant metric dimension, as a significant graph invariant, finds applications in diverse areas such as robust network optimization, autonomous robot navigation and intelligent sensor systems. In this paper, we investigate the fault-tolerant metric dimension and fault-tolerant edge metric dimension of zero-divisor graphs arising from upper triangular matrices over a finite commutative ring. The obtained results contribute to the understanding of metric-based fault tolerance in algebraically structured graphs.

Keywords: fault-tolerant resolving set; fault-tolerant metric dimension; fault-tolerant edge resolving set; fault-tolerant edge metric dimension (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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