Regularity and Planarity of Token Graphs

Abstract

Let $G=(V,E)$ be a graph of order $n$ and let $1\le k<n$ be an integer. The $k$-token graph of $G$ is the graph whose vertices are all the $k$-subsets of $V$, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in $G$. In this paper we characterize precisely, for each value of $k$, which graphs have a regular $k$-token graph and which connected graphs have a planar $k$-token graph.

13 pages, 5 figures. Referee suggestions and corrections incorporated (in particular, a mistake in the proof of Theorem 2.9 was fixed). One reference added. Accepted for publication in "Discussiones Mathematicae Graph Theory"

Cited by in corpus (13)

• Droplet states in quantum XXZ spin systems on general graphs
• On the Connectivity of Token Graphs of Trees
• Hamiltonicity of Token Graphs of some Join Graphs
• The automorphism groups of some token graphs
• Cohen-Macaulayness of triangular graphs
• Independence numbers of some double vertex graphs and pair graphs
• Entanglement Entropy Bounds in the Higher Spin XXZ Chain
• Hamiltonicity of the Double Vertex Graph and the Complete Double Vertex Graph of some Join Graphs
• Well-covered Token Graphs
• On the Laplacian spectra of token graphs
• The Edge-connectivity of Token Graphs
• A study on token digraphs
• On the 4-girth-thickness of the line graph of the complete graph