English

Fundamental Groupoids for Graphs

Combinatorics 2020-07-14 v1

Abstract

In this paper, we develop a ×\times-homotopy fundamental groupoid for graphs, and show a functorial relationship to the 2-category of graphs. We further explore the fundamental groupoid of graph products and develop a groupoid product which respects the graph product. A van Kampen Theorem for these groupoids is provided. Finally, we generalize previous work on a fundamental group for graphs, developing a looped walk groupoid and showing a connection to the polyhedral complex of graph morphisms.

Keywords

Cite

@article{arxiv.2007.06438,
  title  = {Fundamental Groupoids for Graphs},
  author = {Tien Chih and Laura Scull},
  journal= {arXiv preprint arXiv:2007.06438},
  year   = {2020}
}

Comments

arXiv admin note: text overlap with arXiv:1901.01619

R2 v1 2026-06-23T17:04:46.166Z