Metric Dimension of Related Wheel Graphs

Abstract

The metric dimension of a graph is a central concept in graph theory, which deals with de- termining the minimum number of vertices required to uniquely identify every other vertex in the graph through their distances to the selected set of vertices, known as a resolving set. This thesis explores the metric dimension of related wheel graphs, a family of graphs ob- tained by attaching a cycle graph to a central vertex, thus forming a wheel like structure. We examine the metric dimension in both classical and related wheel graphs, where modifica- tions such as additional connections or altered structures are introduced. Through a detailed analysis, we aim to provide bounds on the metric dimension for different classes of related wheel graphs, propose efficient algorithms for finding the resolving set, and compare the metric dimension of these graphs with other well-studied graph families. The results of this study contribute to a deeper understanding of the interplay between graph structure and metric dimension, with potential applications in network design, sensor placement and graph labeling.