The set of vertices with positive curvature in a planar graph with nonnegative curvature

Abstract

In this paper, we give the sharp upper bound for the number of vertices with positive curvature in a planar graph with nonnegative combinatorial curvature. Based on this, we show that the automorphism group of a planar---possibly infinite---graph with nonnegative combinatorial curvature and positive total curvature is a finite group, and give an upper bound estimate for the order of the group.

32 pages, 19 figures

References in corpus (2)

• The Generation of Fullerenes
• On the largest planar graphs with everywhere positive combinatorial curvature (extended arxiv version)