Abstract:
We construct a cyclic path homology theory on digraphs and graphs and describe properties of the introduced homology groups. As an intermediate step, we define the path homology theory on digraphs, which is based on non-self-intersecting paths. We compare the obtained theories with the standard path homology theory and provide examples of computations. Afterwards we apply the obtained results to the investigation of non-self-intersecting cycles in colored (di)graphs.
Key words and phrases:path complex, digraph, path homology, cycles in graph, cycles in digraph, colored digraphs, non-self-intersecting paths, non-self-intersecting cycles, colored graphs.
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