Net Sign Analysis of Eigenvectors and Eigenvalues of the Adjacency Matrices in Graph Theory

圖像理論中鄰接矩陣之本徵值與本徵向量之淨符號分析

李錫隆(Shyi-Long Lee)

《中央研究院化學研究所集刊》 36期 (1989/03) Pp. 93-104

https://doi.org/10.6522/BICAS.1989.36.12

摘要

本文使用淨符號值方法來分析化學圖之鄰接矩陣之本徵向量的圖形特質。探討的模型系統有G_43和b-G_44，其中下標表示點和邊的數目。兩圖形所得的本徵向量所含的拓樸資訊以尖點上加符號的圖和邊上加符號的圖來描述。邊上加符號的圖之淨符號的順序與鄰接矩陣之本徵值的順序一致。這個簡單的分析也運到萘、蒽和焦油腦等實際例子。此法增加我們對Hückel分子軌域中之節面性質之瞭解。

並列摘要

The graphical properties of the eigenvectors of adjacency matrix of a chemical graph are analyzed using net sign approach. Model systems studied are G_(43) and branched G_(44)'; where the subscripts represent the number of vertices and the number of edges. The topological contents stored in these eigenvectors are described using vertex-signed graphs (VSG) and edge-signed graphs (ESG). The relative ordering of net signs of ESG is similar to that of eigenvalues of the adjacency matrix. This simple analysis is also applied to naphthalene, anthracene, and pyrene. It sheds some insight into the not-well-understood nodal properties of Huckel molecular orbital theory.