The equidistant dimension of some graphs of convex polytopes

TL;DR

This paper determines the exact equidistant dimension for specific classes of convex polytope graphs, providing new precise values and bounds for various symmetric graph families.

Contribution

It offers exact values and bounds for the equidistant dimension of several classes of convex polytope graphs, advancing understanding of their metric properties.

Findings

Exact equidistant dimension for $T_n$

Exact values for $R''_n$ and $S''_n$ when $n$ is even

Exact values for $S_n$ when $n$ is odd

Abstract

This paper is devoted to some rotationally symmetric classes of graphs denoted in literature as convex polytope graphs. Exact value of equidistant dimension is found for $T_n$. Next, for even $n$ exact values are found for $R''_n$ and $S''_n$, while for odd $n$ exact value is found for $S_n$. Finally, for odd $n$, lower bound are found for $R''_n$ and $S''_n$.