k圈图的最大Laplace分离度

The maximum Laplacian separator of k-cyclic graph

设G是一个n阶k圈图,k圈图为边数等于顶点数加k-1的简单连通图。μ_(1)(G)、μ_(2)(G)分别记为图G的Laplace矩阵的最大特征值和次大特征值,图G的Laplace分离度定义为S_(L)(G)=μ_(1)(G)-μ_(2)(G)。本文研究了给定阶数的k圈图的最大Laplace分离度,并刻画了相应的极图,其结果推广了已有当k=1,2,3时的结论。

Let G be an n-order k-cyclic graph.The k-cyclic graph is a simply connected graph which the number of edges is equal to the number of vertices adding k-1.Letμ(G)andμ(G)be the largest eigenvalue and the second largest eigenvalue of the Laplacian matrix of G,respectively.The Laplacian separator of graph G is defined as S(G)=μ(G)-μ(G).In this paper,we study the maximun Laplacian separator of k-cyclic graph with given order,and characterize the according extremal graph.The result generalizes the existing conclusions when k=1,2,3.