BARTHOLDI ZETA FUNCTIONS OF PERIODIC SIMPLE GRAPHS

Iwao Sato (Japan)

Received June 16, 2008

Abstract

Recently, Guido et al. [8] defined the Ihara zeta function of a periodic simple graph, and gave a determinant expression of it. We define the Bartholdi zeta function of a periodic simple graph, and present its determinant expression.

Keywords and phrases: zeta function, periodic simple graph, cycle, bump.