單形環面上的等譜問題

Abstract

這篇論文主要是討論特定圖型的等譜性這個古老的圖論問題。其中, 我們將目標放在從PGL(Q1) 的Bruhat-Tits 結構得到的單形環面， 並從他們的zeta 函數中所得的譜來討論哪些單形環面可以被他們的 譜所決定。

The goal of this paper is to discuss the classical isospectral problem in graph theory for a particular type of graphs. We focus on finite regular simplicial tori arising from the Bruhat-Tits building of PGL3(Q1) and study which kinds of simplicial tori can be uniquely determined by their spectra via graph zeta functions.