有向图的胞腔同调
The Cellular Homology of Digraphs
AI总结：
本文在强正则条件下，基于容许条件定义的特殊最小路径，系统引入有向图的胞腔链复形并证明其良定义性，研究胞腔同调性质，并给出示例与观察。
摘要：
在文献[T Y]中，我们研究了在强正则条件下，有向图G的路径复形中的最小路径P及其支撑子有向图Supp(P)的对(P, Supp(P))。本文首先考虑由容许条件（定义[ref]）指定的特殊最小路径P，这意味着(P, Supp(P))允许奇异立方实现。基于这样的子集，我们系统地引入了与G相关的胞腔链复形的定义，并证明了其良定义性。然后我们研究了这种胞腔同调的若干性质。最后，我们给出了几个有趣的例子以及一些重要的观察。
英文摘要：
In \cite{TY}, we investigate the pair $(P, \Supp(P))$ of minimal path $P$ and its supporting sub-digraph $\Supp(P)$ in the path complex of a digraph $G$ under the strongly regular condition. In this paper, first, we consider the special minimal path $P$ specified by the admissible condition (Definition \ref{admpair}), which means that $(P,\Supp(P))$ admits a singular cubical realization. Based on such a subset, we systematically introduce the definitions of cellular chain complex associated to $G$ and prove the well-definedness. Then we study several properties of such cellular homologies. Finally, we present several intriguing examples as well as some important observations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
