An Ihara formula for partially directed graphs
An Ihara formula for partially directed graphs
复制标题
DOI：
10.1016/j.laa.2009.02.006
复制
发表时间：
2009-07
影响因子：
1.1
通讯作者：
Andrei Tarfulea;R. Perlis
中科院分区：
文献类型：
--
作者：
Andrei Tarfulea;R. Perlis
Ihara公式将有限无向图的Ihara zeta函数表示为具有特别好的形式的有理函数。2001年，Mizuno和Sato证明了全有向图的Ihara zeta函数具有类似的表达式，2005年，Sato将Ihara的公式推广到连通、简单、部分有向图。(Sato证明了他的公式为更一般的两个变量巴托尔迪zeta函数。本文对任意有限图的Ihara zeta函数公式给出了一个新的证明，该图不一定是连通的或简单的，无论它是无向的、完全有向的还是部分有向的.
Ihara’s formula expresses the Ihara zeta function of a finite undirected graph as a rational function with a particularly nice form. In 2001 Mizuno and Sato showed that the Ihara zeta function of a fully directed graph has a similar expression, and in 2005, Sato generalized Ihara’s formula to connected, simple, partially directed graphs. (Sato proved his formula for the more-general two-variable Bartholdi zeta function.) This paper provides a new proof of Ihara’s formula for the Ihara zeta function of any finite graph, not necessarily connected or simple, no matter whether it is undirected, fully directed, or partially directed.