Metric dimension of some distance-regular graphs

TL;DR

This paper investigates the metric dimension of various distance-regular graphs by constructing resolving sets and establishing upper bounds, enhancing understanding of graph identification properties.

Contribution

The paper introduces new resolving sets for Johnson, doubled Odd, doubled Grassmann, and twisted Grassmann graphs, providing upper bounds on their metric dimensions.

Findings

Constructed resolving sets for Johnson graphs.

Established upper bounds for doubled Odd graphs.

Provided metric dimension bounds for Grassmann graphs.

Abstract

A resolving set of a graph is a set of vertices with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. In this paper, we construct a resolving set of Johnson graphs, doubled Odd graphs, doubled Grassmann graphs and twisted Grassmann graphs, respectively, and obtain the upper bounds on the metric dimension of these graphs.