The localization number and metric dimension of graphs of diameter 2

Authors

  • Anthony Bonato Toronto Metropolitan University
  • Melissa Huggan Vancouver Island University
  • Trent Marbach Toronto Metropolitan University

Abstract

We consider the localization number and metric dimension of certain graphs of diameter $2$, focusing on families of Kneser graphs and graphs without 4-cycles. For the Kneser graphs with a diameter of $2$, 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 $2$ and polarity graphs.

Author Biography

Anthony Bonato, Toronto Metropolitan University

Department of Mathematics, Professor and Chair

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Published

2023-04-30

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Section

Articles