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

摘要

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