Combinatorial curvature for planar graphs | Zendy

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Combinatorial curvature for planar graphs

Author(s) -

Higuchi Yusuke

Publication year - 2001

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.10004

Subject(s) - mathematics , sectional curvature , curvature , combinatorics , scalar curvature , constant curvature , ricci curvature , planar graph , graph , planar , negative curvature , bounded function , discrete mathematics , pure mathematics , geometry , mathematical analysis , computer science , computer graphics (images)

Regarding an infinite planar graph G as a discrete analogue of a noncompact simply connected Riemannian surface, we introduce the combinatorial curvature of G corresponding to the sectional curvature of a manifold. We show this curvature has the property that its negative values are bounded above by a universal negative constant. We also prove that G is hyperbolic if its curvature is negative. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 220–229, 2001

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