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- W4386875249 abstract "The $k$-token graph $F_k(G)$ of a graph $G$ on $n$ vertices is the graph whose vertices are the ${nchoose k}$ $k$-subsets of vertices from $G$, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in $G$. It is known that the algebraic connectivity (or second Laplacian eigenvalue) of $F_k(G)$ equals the algebraic connectivity $alpha(G)$ of $G$. In this paper, we give some bounds on the (Laplacian) eigenvalues of a $k$-token graph (including the algebraic connectivity) in terms of the $h$-token graph, with $hleq k$. For instance, we prove that if $lambda$ is an eigenvalue of $F_k(G)$, but not of $G$, then $$ lambdage kalpha(G)-k+1. $$ As a consequence, we conclude that if $alpha(G)geq k$, then $alpha(F_h(G))=alpha(G)$ for every $hle k$." @default.
- W4386875249 created "2023-09-20" @default.
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- W4386875249 date "2023-09-16" @default.
- W4386875249 modified "2023-10-16" @default.
- W4386875249 title "Some bounds on the Laplacian eigenvalues of token graphs" @default.
- W4386875249 doi "https://doi.org/10.48550/arxiv.2309.09041" @default.
- W4386875249 hasPublicationYear "2023" @default.
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