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 $x_1{x}_2\dots x_c$ with $x_i\in \{1,2,\dots ,d\}$. 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.