On some metric properties 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.