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Minimal Path and Acyclic Models in the Path Complex

· 2022 · math.AT · arXiv 2208.14063

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abstract

In this paper, firstly, we will study the structure of the path complex $(\Omega_*(G;\Z),\partial)$ of a digraph $G$ via the $\Z$-generators of $\Omega_*(G,\Z)$ under strongly regular condition, which is called the minimal path in \cite{HY}. In particular, we will study various examples of the minimal $3$-paths. Secondly, we will show that the supporting sub-digraph of minimal path has acyclic path homologies. Thirdly, we will consider the applications of such an acyclic model.

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math.AT 1

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2024 1

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CONDITIONAL 1

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Primitive path homology

math.AT · 2024-11-28 · conditional · novelty 6.0

Primitive path homology is a new digraph invariant that coincides with GLMY path homology on asymmetric digraphs and differs on symmetric ones.

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  • Primitive path homology math.AT · 2024-11-28 · conditional · none · ref 19 · internal anchor

    Primitive path homology is a new digraph invariant that coincides with GLMY path homology on asymmetric digraphs and differs on symmetric ones.