Enumeration of connected bipartite graphs with given Betti number

Autor:	Hasui, Taro, Shirai, Tomoyuki, Yabuoku, Satoshi
Rok vydání:	2022
Předmět:	Mathematics - Combinatorics 05A15 05C31 (Primary) 05C30 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We obtain first order linear partial differential equations which are satisfied by exponential generating functions of two variables for the number of connected bipartite graphs with given Betti number. By solving these equations inductively, we obtain the explicit form of generating functions and derive the asymptotic behavior of their coefficients. We also introduce a family of basic graphs to classify connected bipartite graphs and give another expression of the generating functions as the sum over basic graphs of rational functions of those for the number of labeled bipartite rooted spanning trees. Comment: 31 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.03996 Zobrazit plný text záznamu View this record from Arxiv