一个构造等能量图族的方法

A method of constructing families of equienergetic graphs

一个图的能量定义为图的邻接矩阵的特征值的绝对值之和,是一类重要的图指标.利用矩阵性质给出了一类联并图的谱刻划:正则图G1,G2,…,Gn的联并图G[G1,G2,…,Gn]的谱是由正则图G1,G2,…,Gn的谱(去掉每个正则图的第一个最大特征值)和一个由图G决定的辅助矩阵的特征值组成.这个刻划能够给出一个构造等能量图的方法.作为方法的应用,给出一些等能量图的例子.

As an important graph index the energy of a graph is defined as the absolute sum of eigenvalues of the adjacency matrix of the graph.By matrix theory the characterization of the spectrum of a join union graph,that the spectrum of the joined union graph G[G1,G2,…,Gn] generated by regular graphs G1,G2,…,Gn consists of the spectra of G1,G2,…,Gn (except for the first maximal eigenvalue of every Gi) and the eigenvalues of an auxiliary matrix determined by graph G,is given.By this characterization a method of constructing equienergetic graphs is given and,as its application,we give some examples of some equienergetic graphs.