2024/02/08 by Tang, Xinxing, Yau, Shing-Tung
#05C10 #05C20 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #F.2.2 #FOS: Mathematics
paper · doi:10.48550/arxiv.2402.05682
In \citeTY, 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 \refadmpair), 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.