Independence numbers of the 2-token graphs of some join graphs
Luis Manuel Rivera, Gerardo Vazquez Briones

TL;DR
This paper investigates the independence numbers of 2-token graphs derived from join graphs, providing a construction method and calculating these numbers for specific graph families like fan, wheel, and join of an empty graph with a complete graph.
Contribution
It introduces a method to construct large independent sets in 2-token graphs of join graphs and computes their independence numbers for several important graph classes.
Findings
Provides a construction method for independent sets in 2-token graphs of join graphs.
Determines the independence number for 2-token graphs of fan, wheel, and join of empty and complete graphs.
Abstract
The -token graph of a graph is the graph whose set of vertices consists of all the -subsets of , where two vertices are adjacent if and only if their symmetric difference is an edge in . Let be the join graph of and , where is any graph. In this paper, we give a method to construct an independent set of from an independent set of such that . As an application, we obtain the independence number of the -token graphs of fan graphs , wheel graphs and .
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