2017/12/31 by Taichi Kousaka, Kousaka, Taichi
Chemistry · Materials Science · Mathematics · #Analysis of PDEs (math.AP) #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Graphene research and applications #Number Theory (math.NT) #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.1801.00291
openalex publication_date 2017/12/31 · openalex created_date 2018/01/12 · openalex updated_date 2026/07/28
We introduce a generalized Bartholdi zeta function for simple graphs with bounded degree. This zeta function is a generalization of both the Bartholdi zeta function which was introduced by L.~Bartholdi and the Ihara zeta function which was introduced by G.~Chinta, J.~Jorgenson and A.~Karlsson. Furthermore, we establish a Bartholdi type formula of this Bartholdi zeta function for simple graphs with bounded degree. Moreover, for regular graphs, we give a new expression of the heat kernel which is regarded as a one-parameter deformation of the expression obtained by G.~Chinta, J.~Jorgenson and A.~Karlsson. By applying this formula, we give an alternative proof of the Bartholdi zeta function formula for regular graphs.