Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 16 1 2022 01 01 Fundamental groupoids for graphs 221 248 101766 10.52547/cgasa.2021.101766 EN Tien Chih Montana State University-Billings 0000-0002-7278-5180 Laura Scull Fort Lewis College Journal Article 2021 11 29 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. https://cgasa.sbu.ac.ir/article_101766_17f759e56785d9fdeeb27d202b460516.pdf