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arXiv · 2611.08186

On generalized token graphs with tokens of different colors

Cristina Dalfó·Blas Fernández·Miquel Àngel Fiol·Mónica A. Reyes
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Abstract

We generalize the concept of token graphs, and we call them supertoken graphs. In this work, we consider the variant in which tokens are distinguishable (for instance, by color) and at most one token is allowed on each vertex. We formally define this kind of supertoken graphs and present their basic properties. We study their diameter, in which cases they are Cayley graphs, and their spectra. Moreover, we provide bounds or exact values for the independence, the vertex cover, the clique, and the chromatic numbers of these graphs. Finally, we characterize the cases in which the supertoken graphs of complete graphs are planar.

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Cristina Dalfó, Blas Fernández, Miquel Àngel Fiol, Mónica A. Reyes. 2026-11-05. On generalized token graphs with tokens of different colors. https://arxiv.org/abs/2611.08186

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