arXiv subjects

Melissa A. Huggan

Publications and source records attributed to Melissa A. Huggan.

20 records · Page 2Linked to original sources

arXiv2020

The localization number and metric dimension of graphs of diameter 2

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.

math.CO↗

arXiv2020

The localization number of designs

We study the localization number of incidence graphs of designs. In the localization game played on a graph, the cops attempt to determine the location of an invisible robber via distance probes. The localization number of a graph $G$, written $ζ(G)$, is the minimum number of cops needed to ensure the robber's capture. We present bounds on the localization number of incidence graphs of balanced incomplete block designs. Exact values of the localization number are given for the incidence graphs of projective and affine planes. Bounds are given for Steiner systems and for transversal designs.

math.CO↗