Fundamental Groupoids for Graphs
Combinatorics
2020-07-14 v1
Abstract
In this paper, we develop a -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.
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