On Sum of Powers of the Signless Laplacian Eigenvalues of Graphs  ABSTRACT  |  FULL TEXT 

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References

1. Akbari, S., Ghorbani, E., Koolen, J. H. and Oboudi, M. R. On sum of powers of the Lapla- cian and signless Laplacian eigenvalues of graphs, Electron. J. Combin. 17, R115, 2010.
2. Anderson, W. N. and Morley, T. D. Eigenvalues of the Laplacian of a graph, Linear Multi- linear Algebra 18, 141–145, 1985.
3. Chen, Y. Q. and Wang, L. G. Sharp bounds for the largest eigenvalue of the signless Lapla- cian of a graph, Linear Algebra Appl. 433, 908–913, 2010.
4. Cvetkovi´c, D., Rowlinson, P. and Simi´c, S. K. Signless Laplacians of finite graphs, Linear Algebra Appl. 423, 155–171, 2007.
5. Cvetkovi´c, D., Rowlinson, P. and Simi´c, S. K. Eigenvalue bounds for the signless Laplacian, Publ. Inst. Math. (Beograd), 81 (95), 11–27, 2007.
6. Cvetkovi´c, D. and Simi´c, S. K. Towards a spectral theory of graphs based on the signless Laplacian II, Linear Algebra Appl. 432, 2257–2272, 2010.
7. Gutman, I. The energy of a graph, Ber. Math Statist. Sekt. Forschungsz. Graz. 103, 1–22, Gutman, I. Total π-electron energy of benzenoid hydrocarbons, Topics Curr. Chem. 162, –63, 1992.
8. Gutman, I. The energy of a graph: odd and new results, in : A. Betten, A. Kohnert, R. Laue, A. Wassermann (Eds.) (Algebraic Combinatorics and Applications, Springer-Verlag, Berlin, 2001), 196–211.

9. Gutman, I., Kiani, D., Mirzakhah, M. and Zhou, B. On incidence energy of a graph, Linear Algebra Appl. 431, 1223–1233, 2009.
10. Gutman, I. and Mohar, B. The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36, 982–985, 1996.
11. Gutman, I. and Trinajsti´c, N. Graph theory and molecular orbitals, Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17, 535–538, 1972.
12. Gutman, I. and Zhou, B. Laplacian energy of a graph, Linear Algebra Appl. 414, 29–37, Jooyandeh, M. R., Kiani, D. and Mirzakhah, M. Incidence energy of a graph, MATCH Commun. Math. Comput. Chem. 62, 561–572, 2009.
13. Li, J. and Pan, Y. A note on the second largest eigenvalue of the Laplacian matrix of a graph, Linear Multilinear Algebra 48, 117–121, 2000.
14. Liu, J. P. and Liu, B. L. A Laplacian-energy-like invariant of a graph, MATCH Commun. Math. Comput. Chem. 59, 355–372, 2008.
15. Liu, M. H. and Liu, B. L. New sharp upper bounds for the first Zagreb index, MATCH Commun. Math. Comput. Chem. 62, 689–698, 2009.
16. Liu, M. H. and Liu, B. L. The signless Laplacian spread, Linear Algebra Appl. 432 (2-3), –514, 2010.
17. Li, X. L. and Zheng, J. A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem. 54, 195–208, 2005.
18. Marshall, A. W. and Olkin, I. Inequalities, Theory of Majorization and its Applications (Academic Press, New York, 1979).
19. Merris, R. Laplacian matrices of graphs: a survey, Linear Algebra Appl. 197-198, 143–176, Merris, R. Laplacian graph eigenvectors, Linear Algebra Appl. 278, 221–236, 1998.
20. Pavlovi´c, L. Maximal value of the zeroth-order Randi´c index, Discrete Appl. Math. 127, –626, 2003.
21. Stevanovi´c, D., Ili´c, A., Onisor, C. and Diudea, M. LEL–a newly designed molecular de- scriptor, Acta Chim. Slov. 56, 410–417, 2009.
22. Tian, G. X., Huang, T. Z. and Zhou, B. A note on sum of powers of the Laplacian eigenvalues of bipartite graphs, Linear Algebra Appl. 430, 2503–2510, 2009.
23. Zhou, B. On sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra Appl. , 2239–2246, 2008.
24. Zhou, B. On sum of powers of Laplacian eigenvalues and Laplacian Estrada index of graphs, MATCH Commun. Math. Comput. Chem. 62, 611–619, 2009.