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运筹学学报 ›› 2022, Vol. 26 ›› Issue (2): 137-142.doi: 10.15960/j.cnki.issn.1007-6093.2022.02.012

•   • 上一篇    

k圈图的最大Laplace分离度

余桂东1,2,*(), 阮征1, 舒阿秀1   

  1. 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
  • 收稿日期:2019-01-15 出版日期:2022-06-15 发布日期:2022-05-27
  • 通讯作者: 余桂东 E-mail:guidongy@163.com
  • 作者简介:余桂东  E-mail: guidongy@163.com
  • 基金资助:
    国家自然科学基金(11871077);安徽省自然科学基金(1808085MA04);安徽省高校自然科学基金(KJ2020A0894);合肥幼专图论科研创新团队(KCTD202001)

The maximum Laplacian separator of $ k $-cyclic graph

Guidong YU1,2,*(), Zheng RUAN1, Axiu SHU1   

  1. 1. School of Mathematics and Physics, Anqing Normal University, Anqing 246133, Anhui, China
    2. Department of Public Teaching, Hefei Preschool Education College, Hefei 230013, Anhui, China
  • Received:2019-01-15 Online:2022-06-15 Published:2022-05-27
  • Contact: Guidong YU E-mail:guidongy@163.com

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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 $的简单连通图。$ \mu_{1}(G) $、$ \mu_{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)=\mu_{1}(G)-\mu_{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。

关键词: k圈图, Laplace矩阵, Laplace分离度

Abstract:

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 $. Let $ \mu_{1}(G) $ and $ \mu_{2}(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_{L}(G)=\mu_{1}(G)-\mu_{2}(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 $.

Key words: k-cyclic graph, Laplacian matrix, Laplacian separator

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