Exploring the 3-Token Graph of Particular Graphs
Felicia Servina Djuang, Arizka Yuliana, Widi Bagaskara, and Yeni Susanti

TL;DR
This paper explores the properties of 3-token graphs derived from path graphs and disjoint unions, analyzing their structural characteristics and how original graph structures influence the token graphs.
Contribution
It provides a detailed analysis of the structural properties of 3-token graphs from path graphs and their disjoint unions, extending understanding of token graphs in graph theory.
Findings
Analyzed connectivity, diameter, and chromatic number of 3-token graphs.
Extended analysis to 3-token graphs of disjoint unions of graphs.
Contributed to understanding of token graphs and their applications.
Abstract
This study investigates the properties of the 3-token graph derived from path graphs, with a particular focus on its structural characteristics and key attributes. We analyze how the 3-token graph is constructed from path graphs and explore fundamental properties such as connectivity, diameter, and chromatic number. Furthermore, we extend our analysis to the 3-token graph of the disjoint union of two given graphs, examining its unique features and how the structure of the original graphs influences the resulting 3-token graph. The findings of this study contribute to a deeper understanding of token graphs and their applications in graph theory. (We would like to note that an earlier version of this manuscript was previously made available as a preprint on Preprints.org (DOI: 10.20944/preprints202505.1605.v1). The current submission corresponds to the revised version that has been…
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Interconnection Networks and Systems
