Publication Date

Spring 2026

Degree Type

Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics and Statistics

Advisor

Jesse Geneson; Sogol Jahanbekam; Yan Zhang

Abstract

Metric dimension is a graph parameter that measures the smallest distance-based unique coordinate system on a graph. Fault-tolerant metric dimension is a variant that requires redundancy. Inspired by this idea, we propose and investigate a new variant we call error-tolerant metric dimension. We first prove some fundamental results to gain familiarity with this more complex variant. Then, we use these tools to study relative behaviors of error-tolerant metric dimension. We prove explicit computations for simple graph families, including bipartite complete graphs and paths. Finally, we extend extremal results from previous papers on metric dimension, including a full correction of an erroneous result.

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Mathematics Commons

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