Geodesic
Fundamental groupoids of digraphs and graphs
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 35-65.

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We introduce the notion of fundamental groupoid of a digraph and prove its basic properties. In particular, we obtain a product theorem and an analogue of the Van Kampen theorem. Considering the category of (undirected) graphs as the full subcategory of digraphs, we transfer the results to the category of graphs. As a corollary we obtain the corresponding results for the fundamental groups of digraphs and graphs. We give an application to graph coloring.
DOI : 10.21136/CMJ.2018.0683-15
Classification : 05C25, 05C38, 05C76, 20L05, 57M15
Keywords: digraph; fundamental group; fundamental groupoid; product of graphs 
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Grigor'yan, Alexander; Jimenez, Rolando; Muranov, Yuri. Fundamental groupoids of digraphs and graphs. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 35-65. doi : 10.21136/CMJ.2018.0683-15. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0683-15/

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