Top

Journal of Applied Mathematics and Computing

Published in:

01-06-2016 | Original Research

The Laplacian and signless Laplacian spectrum of semi-Cayley graphs over abelian groups

Authors: Xing Gao, Huazhong Lü, Yifei Hao

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2016

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, a formula of the Laplacian and signless Laplacian spectrum of semi-Cayley graphs over abelian groups is given. As applications of our main result, special formulae of Laplacian and signless Laplacian spectrum are also given for two classes of semi-Cayley graphs (one matching bi-Cayley graphs and the join of two Cayley graphs over isomorphic abelian groups). In particular, a method to construct Laplacian and signless Laplacian integral semi-Cayley graphs is obtained.

previous article Existence results for boundary value problems of fractional functional differential equations with delay

next article A modified PRP conjugate gradient algorithm with nonmonotone line search for nonsmooth convex optimization problems

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Anderson, W.N., Morley, T.D.: Eigenvalues of the Laplacian of a graph. Linear Multilinear Algebra Appl. 18, 141–145 (1985)MathSciNetCrossRefMATH

Babai, L.: Spectra of Cayley graphs. J. Combin. Theory Ser. B 27, 180–189 (1979)MathSciNetCrossRefMATH

Bouwer, I.Z., Chernoff, W.W., Monson, B., Star, Z.: The Foster Census. Charles Babbage Research Centre, Winnipeg (1988)

Biggs, N.L.: Algebraic Graph Theorey, 2nd edn. Cambridge University Press, Cambridge (1993)

Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs. Academic Press, New York (1980)MATH

Cvetković, D., Rowlinson, P., Simić, S.K.: Signless Laplacians of finite graphs. Linear Algebra Appl. 423, 155–171 (2007)MathSciNetCrossRefMATH

van Dam, E.R., Haemers, W.: Which graphs are determined by their spectrum? Linear Algebra Appl. 373, 241–272 (2003)MathSciNetCrossRefMATH

Du, S.F., Marušič, D.: Biprimitive graphs of smallest order. J. Algebraic Combin. 9, 151–156 (1999)MathSciNetCrossRefMATH

Gao, X., Luo, Y.F.: The spectrum of semi-Cayley graphs over abelian groups. Linear Algebra Appl. 432, 2974–2983 (2010)MathSciNetCrossRefMATH

10.

Godsil, C.D.: Algebraic Combinatorics. Chapman & Hall, New York (1993)MATH

11.

Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1991)CrossRefMATH

12.

Kovács, I., Malnič, A., Marušič, D., Miklavič, Š.: One-matching bi-Cayley graphs over abelian groups. Eur. J. Comb. 30, 602–616 (2009)MathSciNetCrossRefMATH

13.

Li, C.H.: The finite vertex-primitive and vertex-biprimitive \(s\)-transitive graphs for \(s>4\). Trans. Amer. Math. Soc. 353, 3511–3529 (2001)MathSciNetCrossRefMATH

14.

Li, C.H.: Permutation groups with a cyclic regular subgroup and arc-transitive circulants. J. Algebraic Combin. 21, 131–136 (2005)MathSciNetCrossRefMATH

15.

Merris, R.: Laplacian matrices of graphs: a survey. Linear Algebra Appl. 197–198, 143–176 (1994)MathSciNetCrossRefMATH

16.

Merris, R.: Laplacian graph eigenvectors. Linear Algebra Appl. 278, 221–236 (1998)MathSciNetCrossRefMATH

17.

Newman, M.W.: The laplacian spectrum of graphs, Master thesis, University of Manitoba (2000)

18.

Muzychuk, M.: A solution of the isomorphism problem for circulant graphs. Proc. Lond. Math. Soc. 88, 1–41 (2004)MathSciNetCrossRefMATH

19.

Resmi, M.J.D., Jungnickel, D.: Strongly regular Semi-Cayley graphs. J. Algebraic Combin. 1, 171–195 (1992)MathSciNetCrossRefMATH

20.

So, W.: Integral circulant graphs. Discret. Math. 306, 153–158 (2005)MathSciNetCrossRefMATH

21.

Watkins, M.E.: A theorem on Tait colorings with an application to generalized Petersen graphs. J. Combin. Theory 6, 152–164 (1969)MathSciNetCrossRefMATH

22.

Wilson, R.J.: Introduction to Graph Theory, 3rd edn. Longman Inc., New York (1982)

23.

Xu, J., Qu, R.: The spectra of hypercubes. J. Eng. Math. 16, 1–5 (1999)MathSciNetMATH

24.

Xu, Y.: The spectra of Cayley graphs on abelian groups, Master Thesis, Xinjiang University (2007)

25.

Zhang, X.D.: The signless Laplacian spectral radius of graphs with given degree sequences. Discret. Appl. Math. 157, 2928–2937 (2009)MathSciNetCrossRefMATH

Title: The Laplacian and signless Laplacian spectrum of semi-Cayley graphs over abelian groups
Authors: Xing Gao
Huazhong Lü
Yifei Hao
Publication date: 01-06-2016
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2016
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-015-0911-9

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 1-2/2016

Existence of solutions of four-point boundary value problems for fractional differential equations at resonance

Existence and multiplicity for a system of fractional higher-order two-point boundary value problem

A note on “Quotient structures of intuitionistic fuzzy finite state machines”

Optimal balking strategies for high-priority customers in M/G/1 queues with 2 classes of customers

Generalized Peaceman-Rachford splitting method for separable convex programming with applications to image processing

Dynamics of a periodic switched predator–prey system with hibernation, birth pulse and impulsive harvesting

Premium Partner