The Curvature of Graph Products
Oliver Knill
TL;DR
This paper proves that the curvature at a point in the strong product of two finite simple graphs equals the product of their individual curvatures, providing a clear relationship between graph product and curvature.
Contribution
It establishes a precise formula linking the curvature of a graph product to the curvatures of the component graphs, advancing understanding of geometric properties in graph theory.
Findings
Curvature at a point in the strong product equals the product of individual curvatures.
Provides a formula connecting graph product and curvature.
Enhances understanding of geometric properties in graph theory.
Abstract
We show that the curvature K_(G*H)(x,y) at a point (x,y) in the strong product G*H of two arbitrary finite simple graphs is equal to the product K_G(x) K_H(y) of the curvatures.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Operator Algebra Research · Topological and Geometric Data Analysis