On Generalized Token Graphs
Combinatorics
2026-04-07 v1
Abstract
The vertices of a -token graph of a graph correspond to indistinguishable tokens placed on different vertices of . Changing some conditions on both the nature of the tokens and the number of tokens allowed in each vertex of , we define a generalization of token graphs, which we call generalized token graphs or simply supertoken graphs, which have different applications. Depending on the above conditions, different families of graphs (such as the Cartesian -th power of by itself) are obtained, and we present some of their properties, including order, size, and connectivity.
Cite
@article{arxiv.2604.04845,
title = {On Generalized Token Graphs},
author = {Xiaodi Song and Cristina Dalfó and Miquel Àngel Fiol and Mercè Mora and Shenggui Zhang},
journal= {arXiv preprint arXiv:2604.04845},
year = {2026}
}