## Curvature, Geometry and Spectral Properties of Planar Graphs

- Matthias Keller
- Discrete & Computational Geometry
- 2011

Let G be an infinite plane graph such that G is locally finite and every face of G is bounded by a cycle. Then G is said to be positively curved if, for every vertex x of G, 1− d(x)/2 + Σx∈F 1 |F | > 0, where the summation is taken over all facial cycles F containing x. Note that if G is positively curved then the maximum degree of G is at most 5. As a… (More)

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