Geodesic
Fundamental groupoids of digraphs and graphs
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 35-65 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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

[1] Atkin, R. H.: An algebra for patterns on a complex I. Int. J. Man-Mach. Stud. 6 (1974), 285-307. | DOI | MR

[2] Atkin, R. H.: An algebra for patterns on a complex II. Int. J. Man-Mach. Stud. 8 (1976), 483-498. | DOI | MR

[3] Babson, E., Barcelo, H., Longueville, M. de, Laubenbacher, R.: Homotopy theory of graphs. J. Algebr. Comb. 24 (2006), 31-44. | DOI | MR | JFM

[4] Barcelo, H., Kramer, X., Laubenbacher, R., Weaver, C.: Foundations of a connectivity theory for simplicial complexes. Adv. Appl. Math. 26 (2001), 97-128. | DOI | MR | JFM

[5] Brown, R.: Topology and Groupoids. BookSurge, Charleston (2006). | MR | JFM

[6] Dimakis, A., Müller-Hoissen, F.: Differential calculus and gauge theory on finite sets. J. Phys. A, Math. Gen. 27 (1994), 3159-3178. | DOI | MR | JFM

[7] Dimakis, A., Müller-Hoissen, F.: Discrete differential calculus: Graphs, topologies, and gauge theory. J. Math. Phys. 35 (1994), 6703-6735. | DOI | MR | JFM

[8] Grigor'yan, A., Lin, Y., Muranov, Y., Yau, S.-T.: Homotopy theory for digraphs. Pure Appl. Math. Q. 10 (2014), 619-674. | DOI | MR | JFM

[9] Grigor'yan, A., Lin, Y., Muranov, Y., Yau, S.-T.: Cohomology of digraphs and (undirected) graphs. Asian J. Math. 19 (2015), 887-931. | DOI | MR | JFM

[10] Grigor'yan, A., Muranov, Y. V., Yau, S.-T.: Graphs associated with simplicial complexes. Homology Homotopy Appl. 16 (2014), 295-311. | DOI | MR | JFM

[11] Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002). | MR | JFM

[12] Hell, P., Nešetřil, J.: Graphs and Homomorphisms. Oxford Lecture Series in Mathematics and Its Applications 28, Oxford University Press, Oxford (2004). | DOI | MR | JFM

[13] Spanier, E. H.: Algebraic Topology. Springer, Berlin (1995). | DOI | MR | JFM

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