新单圈图H(p,tK1,m)的拉普拉斯谱刻画

doi:10.15960/j.cnki.issn.1007-6093.2019.01.008

运筹学学报 ›› 2019, Vol. 23 ›› Issue (1): 72-80.doi: 10.15960/j.cnki.issn.1007-6093.2019.01.008

新单圈图H(p,tK_1,m)的拉普拉斯谱刻画

孙秋实, 杨筱韵, 王力工^*, 李希赫, 王朋超

西北工业大学理学院应用数学系, 西安 710072

收稿日期:2017-02-09 出版日期:2019-03-15 发布日期:2019-03-15
通讯作者: 王力工 E-mail:lgwangmath@163.com
基金资助:
国家自然科学基金（No.11871398），陕西省自然科学基础研究计划（No.2018JM1032），国家级大学生创新创业训练计划（No.201610699011）

Laplacian spectral characterizations of new unicyclic graphs H(p,tK_1,m)

SUN Qiushi, YANG Xiaoyun, WANG Ligong^*, LI Xihe, WANG Pengchao

Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an 710072, China

Received:2017-02-09 Online:2019-03-15 Published:2019-03-15

摘要/Abstract

摘要：

设图H（p，tK_1，m）是一个顶点数为p+mt的连通单圈图，它是由圈C_p的依次相邻的t（1 ≤ t ≤ p）个顶点的每一个顶点分别与星K_1，m的中心重合而得到的单圈图.现证明单圈图H（p，p K_1，5），H（p，（p-1）K_1，4）是由它们的拉普拉斯谱确定的，并证明了当p为偶数时，单圈图H（p，2K_1，4），H（p，（p-2）K_1，4），H（p，（p-3）K_1，4）也是由它们的拉普拉斯谱确定的.

关键词: 拉普拉斯矩阵, 拉普拉斯谱确定, 单圈图

Abstract:

Let H(p,tK_1,m) denote an unicyclic graph with p+mt vertices obtained from C_p by attaching the center of star K_1,m to each one of t mutual adjacent vertices of the cycle C_p, respectively. In this paper, we show that the unicyclic graphs H(p,p K_1,5) and H((p,(p-1)K_1,4) are determined by their Laplacian spectra, and if p is an even number, then the unicyclic graphs H(p, 2K_1,4), H(p,(p-2)K_1,4) and H(p,(p-3)K_1,4) are also determined by their Laplacian spectra.

Key words: Laplacian matrix, determined by Laplacian spectrum, unicyclic graph

中图分类号:

孙秋实, 杨筱韵, 王力工, 李希赫, 王朋超. 新单圈图H(p,tK_1,m)的拉普拉斯谱刻画[J]. 运筹学学报, 2019, 23(1): 72-80.

SUN Qiushi, YANG Xiaoyun, WANG Ligong, LI Xihe, WANG Pengchao. Laplacian spectral characterizations of new unicyclic graphs H(p,tK_1,m)[J]. Operations Research Transactions, 2019, 23(1): 72-80.

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新单圈图H(p,tK_1,m)的拉普拉斯谱刻画

Laplacian spectral characterizations of new unicyclic graphs H(p,tK_1,m)

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新单圈图H(p,tK1,m)的拉普拉斯谱刻画

Laplacian spectral characterizations of new unicyclic graphs H(p,tK1,m)

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新单圈图H(p,tK_1,m)的拉普拉斯谱刻画

Laplacian spectral characterizations of new unicyclic graphs H(p,tK_1,m)