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arXiv · 2603.09153

$\partial$-invariant path generators for digraphs

Zhenzhi Li·Wujie Shen
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Abstract

We study the structure of the space $Ω_3(G)$ of $\partial$-invariant 3-paths in a directed graph $G$. We prove that $Ω_3(G)$ admits a basis consisting of trapezohedral paths $τ_m$ ($m \ge 2$) and their merging images. Moreover, we provide an explicit construction of such a basis and, as a consequence, obtain an algorithm with time complexity $O(|V(G)|^5)$ for computing the dimension and a basis of $Ω_3(G)$ for any finite digraph.

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Zhenzhi Li, Wujie Shen. 2026-03-10. $\partial$-invariant path generators for digraphs. https://arxiv.org/abs/2603.09153

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