k圈图的最大Laplace分离度  

The maximum Laplacian separator of k-cyclic graph

作　　者：余桂东 阮征 舒阿秀 YU Guidong;RUAN Zheng;SHU Axiu(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,Anhui,China;Department of Public Teaching,Hefei Preschool Education College,Hefei 230013,Anhui,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133 [2]合肥幼儿师范高等专科学校公共教学部,安徽合肥230013

出　　处：《运筹学学报》2022年第2期137-142,共6页Operations Research Transactions

基　　金：国家自然科学基金(No.11871077);安徽省自然科学基金(No.1808085MA04);安徽省高校自然科学基金(No.KJ2020A0894);合肥幼专图论科研创新团队(No.KCTD202001)。

摘　　要：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.

关 键 词：k圈图 LAPLACE矩阵 Laplace分离度 

分 类 号：O157[理学—数学]