English

The localization number and metric dimension of graphs of diameter 2

Combinatorics 2020-08-12 v1

Abstract

We consider the localization number and metric dimension of certain graphs of diameter 22, focusing on families of Kneser graphs and graphs without 4-cycles. For the Kneser graphs with diameter 22, we find upper and lower bounds for the localization number and metric dimension, and in many cases these parameters differ only by an additive constant. Our results on the metric dimension of Kneser graphs improve on earlier ones, yielding exact values in infinitely many cases. We determine bounds on the localization number and metric dimension of Moore graphs of diameter 22 and polarity graphs.

Keywords

Cite

@article{arxiv.2008.04896,
  title  = {The localization number and metric dimension of graphs of diameter 2},
  author = {Anthony Bonato and Melissa A. Huggan and Trent Marbach},
  journal= {arXiv preprint arXiv:2008.04896},
  year   = {2020}
}