Algebraic connectivity of Kronecker products of line graphs

被引：0

作者：

Chauhan, Shivani ^{[1
]}

Reddy, A. Satyanarayana ^{[1
]}

机构：

[1] Shiv Nadar Inst Eminence, Dept Math, Greater Noida 201314, Uttar Pradesh, India

来源：

DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS | 2024年 / 16卷 / 06期

关键词：

Tree; line graph; Kronecker product of graph; Laplacian matrix; algebraic connectivity; SIGNLESS LAPLACIAN; SPECTRAL THEORY; MATRICES;

D O I：

10.1142/S1793830923500751

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a tree with n vertices and L(X) be its line graph. In this work, we completely characterize the trees for which the algebraic connectivity of L(X) x K-m is equal to m - 1, where x denotes the Kronecker product. We provide a few necessary and sufficient conditions for L(X) x K-m to be Laplacian integral. The algebraic connectivity of L(X) x K-m, where X is a tree of diameter 4 and k-book graph is discussed.

引用

页数：16

共 17 条

[1] On algebraic connectivity of graphs with at most two points of articulation in each block [J].

Bapat, R. B. ;

Lal, A. K. ;

Pati, S. .

LINEAR & MULTILINEAR ALGEBRA, 2012, 60 (04) :415-432

[2] TOWARDS A SPECTRAL THEORY OF GRAPHS BASED ON THE SIGNLESS LAPLACIAN, III [J].

Cvetkovic, Dragos ;

Simic, Slobodan K. .

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2010, 4 (01) :156-166

[3] TOWARDS A SPECTRAL THEORY OF GRAPHS BASED ON THE SIGNLESS LAPLACIAN, I [J].

Cvetkovic, Dragos ;

Simic, Slobodan K. .

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2009, 85 (99) :19-33

[4] Towards a spectral theory of graphs based on the signless Laplacian, II [J].

Cvetkovic, Dragos ;

Simic, Slobodan K. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (09) :2257-2272

[5]

Davis P.J., 1970, Circulant Matrices

[6] Old and new results on algebraic connectivity of graphs [J].

de Abreu, Nair Maria Maia .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 423 (01) :53-73

[7] The smallest eigenvalue of the signless Laplacian [J].

de Lima, Leonardo Silva ;

Oliveira, Carla Silva ;

Maia de Abreu, Nair Maria ;

Nikiforov, Vladimir .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 435 (10) :2570-2584

[8] On graphs whose Laplacian matrices have distinct integer eigenvalues [J].

Fallat, SM ;

Kirkland, SJ ;

Molitierno, JJ ;

Neumann, M .

JOURNAL OF GRAPH THEORY, 2005, 50 (02) :162-174

[9]

FIEDLER M, 1973, CZECH MATH J, V23, P298

[10] THE LAPLACIAN SPECTRUM OF A GRAPH [J].

GRONE, R ;

MERRIS, R ;

SUNDER, VS .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1990, 11 (02) :218-238

← 1 2 →