TY - JOUR ID - 101766 TI - Fundamental groupoids for graphs JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Chih, Tien AU - Scull, Laura AD - Montana State University-Billings AD - Fort Lewis College Y1 - 2022 PY - 2022 VL - 16 IS - 1 SP - 221 EP - 248 KW - Graph KW - homotopy KW - groupoid KW - fundamental group DO - 10.52547/cgasa.2021.101766 N2 - 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. UR - https://cgasa.sbu.ac.ir/article_101766.html L1 - https://cgasa.sbu.ac.ir/article_101766_3bc1a1701be553da8327d97fc712a071.pdf ER -