图的拟拉普拉斯特征多项式的系数

The coefficients of quasi-Laplacian characteristic

设 G 是一简单无向图,C(G)表示 G 的无向关联矩阵,Q(G)=C(G)·C(G)~T,det(λI—Q(G))称为图 G 的拟拉普拉斯特征多项式.该文着重对图的拟拉普拉斯特征多项式的系数进行了研究,给出了图的拟拉普拉斯特征多项式的系数的图论解释,得到了 n 阶连通二部图其拟拉普拉斯特征多项式中一次项的系数的绝对值正好为该图的生成树数目的 n 倍.

Let G be a simple undireeted graph,C(G) denote the undirected incidence matrix of G, Q(G)=C(G),C(G)~T,characteristic polynomial of Q(G)be called the Quasi-Laplacian Charac- teristic Polynomial,and the eigenvalues of Q(G) be called the Quasi-Laplacian spectrum of G.In this paper,we investigate the coefficients of the Quasi-Laplacian characteristic polynomial and show some properties of the Quasi-Laplacian characteristic polynomial.