On some metric properties of supertoken graphs

TL;DR

This paper introduces supertoken graphs, generalizes token graphs, and analyzes their metric properties, providing bounds on metric dimension for these infinite graph families.

Contribution

It defines supertoken graphs, extends token graph concepts, and establishes bounds on their metric dimension, advancing understanding of their metric properties.

Findings

Lower bound on metric dimension for G+(d,c)

Definition and properties of supertoken graphs

Upper bound on metric dimension of supertoken graphs

Abstract

In this paper, we construct two infinite families of graphs $G(d,c)$ and $G^+(d,c)$, where, in both cases, a vertex label is $x_1x_2\ldots x_c$ with $x_i\in\{1,2,\ldots, d\}$. We provide a lower bound on the metric dimension, tight on $G^+(d,c)$. Moreover, we give the definition and properties of the supertoken graphs, a generalization of the well-known token graphs. Finally, we provide an upper bound on the metric dimension of supertoken graphs.