Czechoslovak Mathematical Journal

, Volume 68, Issue 1, pp 35–65 | Cite as

Fundamental groupoids of digraphs and graphs

  • Alexander Grigor’yan
  • Rolando Jimenez
  • Yuri Muranov


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.


digraph fundamental group fundamental groupoid product of graphs 

MSC 2010

05C25 05C38 05C76 20L05 57M15 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  • Alexander Grigor’yan
    • 1
  • Rolando Jimenez
    • 2
  • Yuri Muranov
    • 3
  1. 1.Mathematics DepartmentUniversity of BielefeldBielefeldGermany
  2. 2.Instituto de MatematicasUNAM Unidad OaxacaOaxacaMexico
  3. 3.Faculty of Mathematics and Computer ScienceUniversity of Warmia and MazuryOlsztynPoland

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