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.　©　2018　Elsevier　Inc.