English

On the Colin de Verdiere graph number and penny graphs

Metric Geometry 2020-06-11 v1 Combinatorics

Abstract

The Colin de Verdiere number of graph G, denoted by \mu(G), is a spectral invariant of G that is related to some of its topological properties. For example, \mu(G) \leq 3 iff G is planar. A penny graph is the contact graph of equal-radii disks with disjoint interiors in the plane. In this note we prove lower bounds on \mu(G) when the complement \bar{G} is a penny graph.

Keywords

Cite

@article{arxiv.2006.05197,
  title  = {On the Colin de Verdiere graph number and penny graphs},
  author = {A. Y. Alfakih},
  journal= {arXiv preprint arXiv:2006.05197},
  year   = {2020}
}

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