Halin graphs with positive Lin-Lu-Yau curvature
Kaizhe Chen, Huiqiu Lin, Shiping Liu, Zhe You
TL;DR
This paper classifies all generalized Halin graphs that have positive Lin-Lu-Yau curvature, contributing to the understanding of curvature properties in specific graph classes.
Contribution
It provides a complete classification of generalized Halin graphs with positive Lin-Lu-Yau curvature, a novel result in graph curvature analysis.
Findings
All generalized Halin graphs with positive Lin-Lu-Yau curvature are classified.
The classification reveals structural properties linked to curvature positivity.
The work advances understanding of curvature in planar and polyhedral graphs.
Abstract
Halin graphs constitute an interesting class of planar and polyhedral graphs. A generalized Halin graph is obtained by connecting all leaves of a planar embedding of a tree via a cycle. A Halin graph is a generalized Halin graph having no vertex of degree two. We classify all generalized Halin graphs with positive Lin-Lu-Yau curvature.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds