Let G = (V, E) be a graph of order n and let 1 ≤ 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.
@article{bwmeta1.element.doi-10_7151_dmgt_1959,
author = {Walter Carballosa and Ruy Fabila-Monroy and Jes\'us Lea\~nos and Luis Manuel Rivera},
title = {Regularity and Planarity of Token Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {573-586},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1959}
}
Walter Carballosa; Ruy Fabila-Monroy; Jesús Leaños; Luis Manuel Rivera. Regularity and Planarity of Token Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 573-586. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1959/