Laplacian谱半径和阶数相等的c圈图

The c Cyclic Graph Whose Largest Eigenvalue of Its Laplacian Matrix Equals Its Order

设G是1个无向的简单图,ν表示G的阶数,mG(ν)表示ν作为G的Laplacian矩阵的特征值的重数.得到了Laplacian谱半径等于阶数的所有c圈图,研究了c与mG(ν)之间的关系.给出了当G是森林、单圈图、双圈图、三圈图、四圈图时mG(ν)的取值范围,并确定了mG(ν)(≥1)在该取值范围内取不同值时的所有图.

G is a simple undirected graph of order v. mG（v） denotes the muhiplicity of v being an eigenvalue of Laplacian matrix. In this paper, the c cyclic graph whose largest eigenvalue of its Laplacian matrix equals v is obtained, and the relation of c and raG（V） is studied. Moreover, the range of me（v） is obtained when G is a forest, a unicyclic graph, a bicyclic graph, a tricyclic graph and a tetracyclic graph, respectively, and the graph is determined when me（v） （ ≥1 ） takes different value in its range.