Characterizing threshold graphs with k main signless Laplacian eigenvalues

被引：3

作者：

Vinagre, Cybele T. M. ^{[1
]}

Trevisan, Vilmar ^{[2
]}

Bolckau, Johann ^{[1
]}

Chimelli, Rodrigo ^{[1
]}

机构：

[1] Univ Fed Fluminense, Inst Matemat & Estat, Niteroi, RJ, Brazil

[2] Univ Fed Rio Grande do Sul, Inst Matemat, Porto Alegre, RS, Brazil

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2020年 / 602卷

关键词：

Signless Laplacian matrix; Main eigenvalue; Threshold graph; BICYCLIC GRAPHS; MATRICES;

D O I：

10.1016/j.laa.2020.04.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the number k of main signless Laplacian eigenvalues of a threshold graph on n >= 3 vertices is bounded by n - 2 and we characterize, for any integer 1 <= k <= n - 2, all such graphs with exactly k main signless Laplacian eigenvalues. Moreover, we also determine the number of threshold graphs on n vertices with k main signless Laplacian eigenvalues. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：33 / 45

页数：13

共 20 条

[1] Fast algorithms for computing the characteristic polynomial of threshold and chain graphs [J].

Andelic, M. ;

Simic, S. K. ;

Zivkovic, D. ;

Dolicanin, E. C. .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 332 :329-337

[2]

[Anonymous], 2011, ISRN DISCR MATH, DOI DOI 10.5402/2011/108509

[3]

[Anonymous], 1977, Ann. Discrete Math.

[4] Spectra, signless Laplacian and Laplacian spectra of complementary prisms of graphs [J].

Cardoso, Domingos M. ;

Carvalho, Paula ;

de Freitas, Maria Aguieiras A. ;

Vinagre, Cybele T. M. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 544 :325-338

[5] Exponentially many graphs have a Q-cospectral mate [J].

Carvalho, Joao ;

Souza, Bruna S. ;

Trevisan, Vilmar ;

Tura, Fernando C. .

DISCRETE MATHEMATICS, 2017, 340 (09) :2079-2085

[6] Trees, Unicyclic Graphs and Bicyclic Graphs with Exactly Two Q-main Eigenvalues [J].

Chen, Lin ;

Huang, Qiong Xiang .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2013, 29 (11) :2193-2208

[7]

Cvetkovic D., PUBL I MATH BEOGRAD, V85

[8]

Cvetkovic D.M., 1970, PUBL ELEKTROTEH FAK, V320, P27

[9]

Cvetkovic D. M., 1971, Publ. Elektroteh. Fak. Univ. Beogr. Ser. Mat. Fiz., V354, P1

[10] Signless Laplacians of finite graphs [J].

Cvetkovic, Dragos ;

Rowlinson, Peter ;

Simic, Slobodan K. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 423 (01) :155-171

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