On the Automorphism Group of Token Graphs of Complete Bipartite Graphs
Ruy Fabila-Monroy, Ana Laura Trujillo-Negrete

TL;DR
This paper determines the automorphism group of the $k$-token graph derived from complete bipartite graphs, providing insights into their symmetry properties and structural automorphisms.
Contribution
It explicitly characterizes the automorphism group of the $k$-token graph of $K_{m,n}$, a problem previously unresolved.
Findings
Automorphism group of $k$-token graphs of $K_{m,n}$ is explicitly determined.
Results reveal symmetry structures depend on the bipartite partition sizes.
Provides foundational understanding for symmetry analysis in token graphs.
Abstract
Let be a graph of order and let . The -token graph of is the graph, whose vertices are all the -subsets of vertices of , where two such -sets are adjacent whenever their symmetric difference is an edge of . In this paper, we determine the automorphism group of the -token graph of the complete bipartite graph .
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · Graph theory and applications
