DOI QR코드

DOI QR Code

The Signless Laplacian Spectral Radius of Unicyclic Graphs with Graph Constraints

  • Feng, Lihua (School of Mathematics, Shandong Institute of Business and Technology) ;
  • Yu, Guihai (School of Mathematics, Shandong Institute of Business and Technology)
  • 투고 : 2007.12.07
  • 심사 : 2008.05.16
  • 발행 : 2009.03.31

초록

In this paper, we study the signless Laplacian spectral radius of unicyclic graphs with prescribed number of pendant vertices or independence number. We also characterize the extremal graphs completely.

키워드

참고문헌

  1. R. B. Bapat, J. W. Grossman, D. M. Kulkarni, Generalized matrix tree theorem for mixed graphs, Linear and Multilinear Algebra, 46(4)(1999), 299-312. https://doi.org/10.1080/03081089908818623
  2. D. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs, Academic Press, New York, 1980.
  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, Signless Laplacians of finite graphs, Linear Algebra Appl., 423(2007), 155-171. https://doi.org/10.1016/j.laa.2007.01.009
  5. 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
  6. 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
  7. L. Feng, Q. Li, X. D. Zhang, Minimizing the Laplacian spectral radius of trees with given matching number, Linear Multilinear Algebra, 55(2)(2007), 199-207. https://doi.org/10.1080/03081080600790040
  8. L. Feng, G. Yu, No starlike trees are Laplacian cospectral, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat, 18(2007), 46-51.
  9. 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
  10. 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
  11. R. Merris, A note on Laplacian graph eigenvalues, Linear Algebra Appl., 285(1-3)(1998), 33-35. https://doi.org/10.1016/S0024-3795(98)10148-9
  12. D. B. West, Introduction to Graph Theory, Prentice-Hall, 2001.

피인용 문헌

  1. 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
  2. Towards a spectral theory of graphs based on the signless Laplacian, II vol.432, pp.9, 2010, https://doi.org/10.1016/j.laa.2009.05.020
  3. Bounds and conjectures for the signless Laplacian index of graphs vol.432, pp.12, 2010, https://doi.org/10.1016/j.laa.2010.01.027
  4. Permanental Bounds for the Signless Laplacian Matrix of a Unicyclic Graph with Diameter d vol.28, pp.4, 2012, https://doi.org/10.1007/s00373-011-1057-7
  5. Color signless Laplacian energy of graphs vol.14, pp.2, 2017, https://doi.org/10.1016/j.akcej.2017.02.003