Year: 2025
Type: article
Abstract: Let G be a connected graph on n vertices and $$1 \le k \le n-1$$ 1 ≤ k ≤ n - 1 an integer. The k -token graph of G is the graph $$F_k(G)$$ F k ( G ) , whose vertices are all the k -subsets of vertices of G , two of which are adjacent whenever their symmetric difference is an edge of G . Every automorphism of G induces an automorphism of $$F_k(G)$$ F k ( G ) in a natural way. Suppose that $$S:=\{x,y\}$$ S : = { x , y } is a cut set of G , such that x and y have the same neighbours in $$G\setminus \{x,y\}$$ G \ { x , y } . In this paper, we show that there exists a large number of automorphisms of $$F_k(G)$$ F k ( G ) defined by S that are not induced by automorphisms of G . We also describe the group produced by all such 2-cuts of G .
Source: Graphs and Combinatorics
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,190
OpenAlex ID: W4416951838