Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

The Signless Laplacian Spectral Radius for Bicyclic Graphs with κ Pendant Vertices

  • Feng, Lihua (School of Mathematics, Shandong Institute of Business and Technology)
  • Received : 2009.08.03
  • Accepted : 2009.10.09
  • Published : 2010.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.

Keywords

References

  1. J. A. Bondy, U.S.R. Murty, Graph Theory with Applications, Macmillan Press, New York, 1976.
  2. D. Cvetkovic, S.K. Simic, Towards a spectral theory of graphs based on the signless Laplacian, Publ. Inst. Math. (Beograde), 85(99),19-33. https://doi.org/10.2298/PIM0999019C
  3. D. Cvetkovic, Signless Laplacians and line graphs, Bull. Acad. Serbe Sci.Ars. Cl. Sci. Math. Nat. Sci. Math., 131(30)(2005), 85-92.
  4. D. Cvetkovic, P.Rowlinson, S.K.Simic, Eigenvalue bounds for the signless Laplacian, Publ. Inst. Math. (Beograd), 81(95)(2007), 11-27.
  5. D. Cvetkovic, P. Rowlinson, S. K. Simic, Signless Laplacians of finite graphs, Linear Algebra Appl., 423(2007), 155-171. https://doi.org/10.1016/j.laa.2007.01.009
  6. M. Desai, V. Rao, A characterizaion of the smallest eigenvalue of a graph, J. Graph Theory, 18(1994), 181-194. https://doi.org/10.1002/jgt.3190180210
  7. 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. https://doi.org/10.1080/03081080701306589
  8. 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. https://doi.org/10.1080/03081080600790040
  9. L. Feng, Q. Li, X. Zhang, Some sharp upper bounds on the spectral radius of graphs, Taiwanese J. Math., 11(2007), 989-997. https://doi.org/10.11650/twjm/1500404797
  10. L. Feng, G. Yu, No starlike trees are Laplacian cospectral, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 18(2007), 46-51.
  11. L. Feng, G. Yu, The signless Laplacian spectral radius of graphs with given diameter, Utilitas Mathematica, to appear.
  12. J. W. Grossman, D.M. Kulkarni, I.Schochetman, Algebraic graph theory without orientation, Linear Algebra Appl. 212/213(1994), 289-307. https://doi.org/10.1016/0024-3795(94)90407-3
  13. J. Guo, The Laplacian spectral radius of a graph under perturbation, Comput. Math. Appl., 54(2007), 709-720. https://doi.org/10.1016/j.camwa.2007.02.009
  14. R. Grone, R. Merris, V. S. Sunder. The Laplacian spectrum of a graph, SIAM J. Matrix Anal. Appl., 11(1990), 218-238. https://doi.org/10.1137/0611016
  15. R. Grone, R. Merris, The Laplacian spectrum of a graph II, SIAM J. Discrete Math., 7(1994), 221-229. https://doi.org/10.1137/S0895480191222653
  16. 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. https://doi.org/10.1016/j.laa.2005.05.022
  17. 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.
  18. C.X. He, J.Y. Shao, J.L. He, On the Laplacian spectral radii of bicyclic graphs, Discrete Math., 308(2008), 5981-5995. https://doi.org/10.1016/j.disc.2007.11.016
  19. 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. https://doi.org/10.1016/j.disc.2005.04.001
  20. R. Merris, Laplacian matrices of graphs: a survey, Linear Algebra Appl., 197/198(1994), 143-176. https://doi.org/10.1016/0024-3795(94)90486-3

Cited by

  1. Spectral analogues of Erdős’ and Moon–Moser’s theorems on Hamilton cycles vol.64, pp.11, 2016, https://doi.org/10.1080/03081087.2016.1151854
  2. The (signless) Laplacian spectral radii of c-cyclic graphs with n vertices, girth g and k pendant vertices vol.65, pp.5, 2017, https://doi.org/10.1080/03081087.2016.1211082
  3. The signless Laplacian spectral radius of tricyclic graphs and trees with k pendant vertices vol.435, pp.4, 2011, https://doi.org/10.1016/j.laa.2011.02.002