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Matematicheskie Zametki, 2021, Volume 109, Issue 5, Pages 705–722
DOI: https://doi.org/10.4213/mzm12599 (Mi mzm12599) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Homology of Digraphs

A. A. Grigor'yanab, Yu. V. Muranovc, R. B. Jimenezd

a Bielefeld University
b V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
c University of Warmia and Mazury in Olsztyn
d National Autonomous University of Mexico, Institute of Mathematics
Full-text PDF (622 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm12599
Abstract: A theory of singular cubic homology of digraphs is developed; the obtained homology groups are proved to be functorial and homotopy invariant. Commutative diagrams of exact sequences similar to the classical ones are constructed, and a relationship between the cubic homology and the path homology of a digraph is described. Carrying over the results to graphs, multigraphs, and quivers is discussed.
Keywords: homology of digraphs, singular cubic homology, path homology, cubic graphs.
Funding agency Grant number
CONACYT - Consejo Nacional de Ciencia y Tecnología 284621
Deutsche Forschungsgemeinschaft SFB 1283
This work was supported by the Collaborative Research Center SFB 1283 and by the National Council for Science and Technology (CONACYT) under grant 284621.
Received: 31.10.2019
Revised: 20.07.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 5, Pages 712–726
DOI: https://doi.org/10.1134/S0001434621050059
Bibliographic databases:
Document Type: Article
UDC: 515.14+519.17
Language: Russian
Citation: A. A. Grigor'yan, Yu. V. Muranov, R. B. Jimenez, “Homology of Digraphs”, Mat. Zametki, 109:5 (2021), 705–722; Math. Notes, 109:5 (2021), 712–726
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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