Dehn colorings and vertex-weight invariants for spatial graphs
Kanako Oshiro, Natsumi Oyamaguchi
TL;DR
This paper introduces vertex-weight invariants for spatial graphs based on Dehn colorings, providing a new method to distinguish spatial graphs that traditional invariants cannot differentiate.
Contribution
It presents a novel class of invariants called vertex-weight invariants, expanding the tools for analyzing and distinguishing spatial graphs.
Findings
Vertex-weight invariants can distinguish certain spatial graphs.
Examples show invariants differentiate graphs beyond link and Dehn coloring counts.
New invariants enhance the classification of spatial graphs.
Abstract
In this paper, we study Dehn colorings for spatial graphs, and give a family of spatial graph invariants that are called vertex-weight invariants. We give some examples of spatial graphs that can be distinguished by a vertex-weight invariant, whereas distinguished by neither their constituent links nor the number of Dehn colorings.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology