Fundamental groupoids of digraphs and graphs |
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| Authors: | Alexander Grigor’yan Rolando Jimenez Yuri Muranov |
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| Institution: | 1.Mathematics Department,University of Bielefeld,Bielefeld,Germany;2.Instituto de Matematicas,UNAM Unidad Oaxaca,Oaxaca,Mexico;3.Faculty of Mathematics and Computer Science,University of Warmia and Mazury,Olsztyn,Poland |
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| Abstract: | 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. |
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