English

On Generalized Token Graphs

Combinatorics 2026-04-07 v1

Abstract

The vertices of a kk-token graph of a graph GG correspond to kk indistinguishable tokens placed on kk different vertices of GG. Changing some conditions on both the nature of the tokens and the number of tokens allowed in each vertex of GG, 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 kk-th power of GG by itself) are obtained, and we present some of their properties, including order, size, and connectivity.

Keywords

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}
}