Fundamental groupoids for graphs

Document Type : Research Paper

Authors

1 Montana State University-Billings

2 Fort Lewis College

Abstract

In recent years several notions of discrete homotopy for graphs have been introduced, including a notion of ×-homotopy due to Dochtermann. In this paper, we define a ×-homotopy fundamental groupoid for graphs, and prove that it is a functorial ×-homotopy invariant for finite graphs. We also introduce tools to compute this fundamental groupoid, including a van Kampen theorem. We conclude with a comparison with previous definitions along these lines, including those built on polyhedral complexes of graph morphisms.

Keywords

References

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Categories and General Algebraic Structures with Applications
Volume 16, Issue 1
January 2022
Pages 221-248

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