On supertoken graphs

TL;DR

This paper introduces supertoken graphs, a generalization of token graphs allowing multiple tokens per vertex, and explores their properties, bounds, and a new infinite family with spectral analysis.

Contribution

It formally defines supertoken graphs, establishes their basic properties, and constructs a new infinite family with spectral analysis.

Findings

Bounds and exact values for independence, clique, and chromatic numbers.

Introduction of the $p$-augmented 2-token graphs of cycles.

Analysis of spectral radius of the new graph family.

Abstract

We generalize the concept of token graphs to obtain supertoken graphs. In the latter case, there can be more than one token in a vertex. We formally define supertoken graphs and establish their basic properties. Moreover, we provide some bounds and exact values on the independence number, clique number, and chromatic number of these graphs. Finally, we construct a new infinite family of graphs, which we call the $p$-augmented 2-token graphs of cycles, and study their properties, including the spectral radius or largest adjacency eigenvalue.