Abstract
The Colin de Verdiere number of graph G, denoted by μ(G), is a spectral invariant of G that is related to some of its topological properties. For example, μ(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 μ(G) when the complement \bar{G} is a penny graph.
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