Two Proofs of Ihara’s Theorem
Two Proofs of Ihara’s Theorem
复制标题
伊原定理的两个证明
DOI：
10.1007/978-1-4612-1544-8_19
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发表时间：
1999
影响因子：
1.6
通讯作者：
S. Northshield
中科院分区：
文献类型：
--
作者：
S. Northshield
证明了对于有限正则图，Ihara的Zeta函数的倒数可以表示为一个简单的多项式乘以一个涉及图的邻接矩阵的行列式。第一个证明是基于用某些多项式来表示正则树上的径向对称特征函数。第二个证明是由于正则树上邻接算子的预解式是指数的。
We give two proofs that, for a finite regular graph, the reciprocal of Ihara’s zeta function can be expressed as a simple polynomial times a determinant involving the adjacency matrix of the graph. The first proof is based on representing radial symmetric eigenfunctions on regular trees in terms of certain polynomials. The second proof is a consequence of the fact that the resolvent of the adjacency operator on regular trees is exponential.