Metric Dimension of Generalized Theta Graphs

2025/10/14 by Benakli, Nadia, Froitzheim, Nicole, Martinez, David
#05C12 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.12100

Abstract

A vertex w in a graph G is said to resolve two vertices u and v if d(w,u)≠ d(w, v). A set W of vertices is a resolving set for G if every pair of distinct vertices is resolved by some vertex in W. The metric dimension of G is the minimum cardinality of such a set. In this paper, we investigate the metric dimension of generalized theta graphs, providing exact values and structural insights for several subclasses.

Citations

• Metric dimensions of bicyclic graphs with potential applications in Supply Chain Logistics
• Remarks on the vertex and the edge metric dimension of 2-connected\n graphs
• Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results
• Getting the Lay of the Land in Discrete Space: A Survey of Metric Dimension and its Applications
• Vertex and edge metric dimensions of unicyclic graphs

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