Regularity and Planarity of Token Graphs - Carballosa Walter; Fabila-Monroy Ruy; Leaños Jesús; Rivera Luis Manuel (Discussiones Mathematicae Graph Theory, 2017)
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.