Path homology theory of edge-colored graphs
In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-col...
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De Gruyter
2021
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oai:doaj.org-article:e7a44c1688f642cbbf7f232ddf74e7522021-12-05T14:10:53ZPath homology theory of edge-colored graphs2391-545510.1515/math-2021-0049https://doaj.org/article/e7a44c1688f642cbbf7f232ddf74e7522021-07-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0049https://doaj.org/toc/2391-5455In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.Muranov Yuri V.Szczepkowska AnnaDe Gruyterarticlepath homology groupsedge coloringedge-colored pathhomotopy-colored graphsspectral sequence05c1505c2005c2505c3805c7618g6018g4055u9957m15MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 706-723 (2021) |
| institution |
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| collection |
DOAJ |
| language |
EN |
| topic |
path homology groups edge coloring edge-colored path homotopy-colored graphs spectral sequence 05c15 05c20 05c25 05c38 05c76 18g60 18g40 55u99 57m15 Mathematics QA1-939 |
| spellingShingle |
path homology groups edge coloring edge-colored path homotopy-colored graphs spectral sequence 05c15 05c20 05c25 05c38 05c76 18g60 18g40 55u99 57m15 Mathematics QA1-939 Muranov Yuri V. Szczepkowska Anna Path homology theory of edge-colored graphs |
| description |
In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences. |
| format |
article |
| author |
Muranov Yuri V. Szczepkowska Anna |
| author_facet |
Muranov Yuri V. Szczepkowska Anna |
| author_sort |
Muranov Yuri V. |
| title |
Path homology theory of edge-colored graphs |
| title_short |
Path homology theory of edge-colored graphs |
| title_full |
Path homology theory of edge-colored graphs |
| title_fullStr |
Path homology theory of edge-colored graphs |
| title_full_unstemmed |
Path homology theory of edge-colored graphs |
| title_sort |
path homology theory of edge-colored graphs |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/e7a44c1688f642cbbf7f232ddf74e752 |
| work_keys_str_mv |
AT muranovyuriv pathhomologytheoryofedgecoloredgraphs AT szczepkowskaanna pathhomologytheoryofedgecoloredgraphs |
| _version_ |
1718371633991778304 |