Advanced SearchSearch Tips
The Signless Laplacian Spectral Radius for Bicyclic Graphs with κ Pendant Vertices
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 50, Issue 1,  2010, pp.109-116
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2010.50.1.109
 Title & Authors
The Signless Laplacian Spectral Radius for Bicyclic Graphs with κ Pendant Vertices
Feng, Lihua;
  PDF(new window)
In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.
Bicyclic graph;signless Laplacian;spectral radius;pendant vertex;
 Cited by
Spectral analogues of Erdős’ and Moon–Moser’s theorems on Hamilton cycles, Linear and Multilinear Algebra, 2016, 64, 11, 2252  crossref(new windwow)
The (signless) Laplacian spectral radii of c-cyclic graphs with n vertices, girth g and k pendant vertices, Linear and Multilinear Algebra, 2017, 65, 5, 869  crossref(new windwow)
The signless Laplacian spectral radius of tricyclic graphs and trees with k pendant vertices, Linear Algebra and its Applications, 2011, 435, 4, 811  crossref(new windwow)
J. A. Bondy, U.S.R. Murty, Graph Theory with Applications, Macmillan Press, New York, 1976.

D. Cvetkovic, S.K. Simic, Towards a spectral theory of graphs based on the signless Laplacian, Publ. Inst. Math. (Beograde), 85(99),19-33. crossref(new window)

D. Cvetkovic, Signless Laplacians and line graphs, Bull. Acad. Serbe Sci.Ars. Cl. Sci. Math. Nat. Sci. Math., 131(30)(2005), 85-92.

D. Cvetkovic, P.Rowlinson, S.K.Simic, Eigenvalue bounds for the signless Laplacian, Publ. Inst. Math. (Beograd), 81(95)(2007), 11-27.

D. Cvetkovic, P. Rowlinson, S. K. Simic, Signless Laplacians of finite graphs, Linear Algebra Appl., 423(2007), 155-171. crossref(new window)

M. Desai, V. Rao, A characterizaion of the smallest eigenvalue of a graph, J. Graph Theory, 18(1994), 181-194. crossref(new window)

Y. Fan, B.S. Tam, J. Zhou, Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order, Linear Multilinear Algebra, 56(2008), 381-397. crossref(new window)

L. Feng, Q. Li, X. Zhang, Minimizing the Laplacian spectral radius of trees with given matching number, Linear and Multilinear Algebra, 55(2007), 199-207. crossref(new window)

L. Feng, Q. Li, X. Zhang, Some sharp upper bounds on the spectral radius of graphs, Taiwanese J. Math., 11(2007), 989-997. crossref(new window)

L. Feng, G. Yu, No starlike trees are Laplacian cospectral, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 18(2007), 46-51.

L. Feng, G. Yu, The signless Laplacian spectral radius of graphs with given diameter, Utilitas Mathematica, to appear.

J. W. Grossman, D.M. Kulkarni, I.Schochetman, Algebraic graph theory without orientation, Linear Algebra Appl. 212/213(1994), 289-307. crossref(new window)

J. Guo, The Laplacian spectral radius of a graph under perturbation, Comput. Math. Appl., 54(2007), 709-720. crossref(new window)

R. Grone, R. Merris, V. S. Sunder. The Laplacian spectrum of a graph, SIAM J. Matrix Anal. Appl., 11(1990), 218-238. crossref(new window)

R. Grone, R. Merris, The Laplacian spectrum of a graph II, SIAM J. Discrete Math., 7(1994), 221-229. crossref(new window)

S. G. Guo, The spectral radius of unicyclic and bicyclic graphs with n vertices and $\kappa$ pendant vertices, Linear Algebra Appl., 408(2005), 78-85. crossref(new window)

S.G. Guo, The largest eigenvalues of the Laplacian matrices of unicyclic graphs, Appl. Math. J. Chinese Univ. Ser. A, 16(2001), no. 2, 131-135. (in Chinese) MR2002b:05096.

C.X. He, J.Y. Shao, J.L. He, On the Laplacian spectral radii of bicyclic graphs, Discrete Math., 308(2008), 5981-5995. crossref(new window)

Y. Hong, X.-D. Zhang, Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees, Discrete Math., 296(2005), 187-197. crossref(new window)

R. Merris, Laplacian matrices of graphs: a survey, Linear Algebra Appl., 197/198(1994), 143-176. crossref(new window)