On the Laplacian integral tricyclic graphs

被引：8

作者：

Huang, Xueyi ^{[1
]}

Huang, Qiongxiang ^{[1
]}

Wen, Fei ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2015年 / 63卷 / 07期

关键词：

tricyclic graph; Laplacian integral graph; algebraic connectivity; 05C50; R-PARTITE GRAPHS; ALGEBRAIC CONNECTIVITY; EIGENVALUES; MATRICES; SPECTRUM;

D O I：

10.1080/03081087.2014.936436

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A graph is called Laplacian integral if all its Laplacian eigenvalues are integers. In this paper, we give an edge subdividing theorem for Laplacian eigenvalues of a graph (Theorem 2.1) and characterize a class of k-cyclic graphs whose algebraic connectivity is less than one. Using these results, we determine all the Laplacian integral tricyclic graphs. Furthermore, we show that all the Laplacian integral tricyclic graphs are determined by their Laplacian spectra.

引用

页码：1356 / 1371

页数：16

共 50 条

[41] On the Laplacian spectra of token graphs
Dalfo, C.
Duque, F.
Fabila-Monroy, R.
Fiol, M. A.
Huemer, C.
Trujillo-Negrete, A. L.
Zaragoza Martinez, F. J.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 625 : 322 - 348
[42] ON GRAPHS WITH THE LARGEST LAPLACIAN INDEX
Liu, Bolian
Chen, Zhibo
Liu, Muhuo
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2008, 58 (04) : 949 - 960
[43] An improved result on Laplacian spectral ratio of connected graphs
Lin, Zhen
Miao, Lianying
JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES, 2021, 42 (04) : 711 - 718
[44] ON THE LAPLACIAN SPECTRA OF PRODUCT GRAPHS
Barik, S.
Bapat, R. B.
Pati, S.
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2015, 9 (01) : 39 - 58
[45] On graphs with the largest Laplacian index
Bolian Liu
Zhibo Chen
Muhuo Liu
Czechoslovak Mathematical Journal, 2008, 58 : 949 - 960
[46] On the Laplacian index of tadpole graphs
Braga, Rodrigo O.
Veloso, Bruno S.
SPECIAL MATRICES, 2024, 12 (01):
[47] On the spectra of tricyclic graphs
Liu, Ruifang
Jia, Huicai
Shu, Jinlong
ARS COMBINATORIA, 2011, 100 : 19 - 32
[48] Bounds on Laplacian eigenvalues related to total and signed domination of graphs
Shi, Wei
Kang, Liying
Wu, Suichao
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2010, 60 (02) : 315 - 325
[49] 'Hubs-repelling' Laplacian and related diffusion on graphs/networks
Estrada, Ernesto
LINEAR ALGEBRA AND ITS APPLICATIONS, 2020, 596 (596) : 256 - 280
[50] Sign-changing diagonal perturbations of Laplacian matrices of graphs
Stehlik, Petr
Vanek, Petr
LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 531 : 64 - 82

← 1 2 3 4 5 →