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The localization number and metric dimension of graphs of diameter 2

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arxiv 2008.04896 v1 pith:YX64FADF submitted 2020-08-11 math.CO

Anthony Bonato , Melissa A. Huggan , Trent Marbach This is my paper · ORCID
classification math.CO
keywords graphsdimensionmetricdiameterlocalizationnumberkneserbounds
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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 diameter $2$, 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.

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