# Fundamental groupoids of digraphs and graphs

Alexander Grigor'yan; Rolando Jimenez; Yuri Muranov

Czechoslovak Mathematical Journal (2018)

- Volume: 68, Issue: 1, page 35-65
- ISSN: 0011-4642

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topGrigor'yan, Alexander, Jimenez, Rolando, and Muranov, Yuri. "Fundamental groupoids of digraphs and graphs." Czechoslovak Mathematical Journal 68.1 (2018): 35-65. <http://eudml.org/doc/294469>.

@article{Grigoryan2018,

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.},

author = {Grigor'yan, Alexander, Jimenez, Rolando, Muranov, Yuri},

journal = {Czechoslovak Mathematical Journal},

keywords = {digraph; fundamental group; fundamental groupoid; product of graphs},

language = {eng},

number = {1},

pages = {35-65},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Fundamental groupoids of digraphs and graphs},

url = {http://eudml.org/doc/294469},

volume = {68},

year = {2018},

}

TY - JOUR

AU - Grigor'yan, Alexander

AU - Jimenez, Rolando

AU - Muranov, Yuri

TI - Fundamental groupoids of digraphs and graphs

JO - Czechoslovak Mathematical Journal

PY - 2018

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 68

IS - 1

SP - 35

EP - 65

AB - 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.

LA - eng

KW - digraph; fundamental group; fundamental groupoid; product of graphs

UR - http://eudml.org/doc/294469

ER -

## References

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