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

Year 2012, Volume: 41 Issue: 4, 527 - 536, 01.04.2012

References

  • 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.
  • Anderson, W. N. and Morley, T. D. Eigenvalues of the Laplacian of a graph, Linear Multi- linear Algebra 18, 141–145, 1985.
  • 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.
  • Cvetkovi´c, D., Rowlinson, P. and Simi´c, S. K. Signless Laplacians of finite graphs, Linear Algebra Appl. 423, 155–171, 2007.
  • 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.
  • 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.
  • 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.
  • 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.
  • Gutman, I., Kiani, D., Mirzakhah, M. and Zhou, B. On incidence energy of a graph, Linear Algebra Appl. 431, 1223–1233, 2009.
  • Gutman, I. and Mohar, B. The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36, 982–985, 1996.
  • 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.
  • 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.
  • 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.
  • Liu, J. P. and Liu, B. L. A Laplacian-energy-like invariant of a graph, MATCH Commun. Math. Comput. Chem. 59, 355–372, 2008.
  • 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.
  • Liu, M. H. and Liu, B. L. The signless Laplacian spread, Linear Algebra Appl. 432 (2-3), –514, 2010.
  • 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.
  • Marshall, A. W. and Olkin, I. Inequalities, Theory of Majorization and its Applications (Academic Press, New York, 1979).
  • 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.
  • Pavlovi´c, L. Maximal value of the zeroth-order Randi´c index, Discrete Appl. Math. 127, –626, 2003.
  • 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.
  • 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.
  • Zhou, B. On sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra Appl. , 2239–2246, 2008.
  • Zhou, B. On sum of powers of Laplacian eigenvalues and Laplacian Estrada index of graphs, MATCH Commun. Math. Comput. Chem. 62, 611–619, 2009.

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

Year 2012, Volume: 41 Issue: 4, 527 - 536, 01.04.2012

References

  • 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.
  • Anderson, W. N. and Morley, T. D. Eigenvalues of the Laplacian of a graph, Linear Multi- linear Algebra 18, 141–145, 1985.
  • 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.
  • Cvetkovi´c, D., Rowlinson, P. and Simi´c, S. K. Signless Laplacians of finite graphs, Linear Algebra Appl. 423, 155–171, 2007.
  • 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.
  • 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.
  • 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.
  • 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.
  • Gutman, I., Kiani, D., Mirzakhah, M. and Zhou, B. On incidence energy of a graph, Linear Algebra Appl. 431, 1223–1233, 2009.
  • Gutman, I. and Mohar, B. The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36, 982–985, 1996.
  • 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.
  • 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.
  • 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.
  • Liu, J. P. and Liu, B. L. A Laplacian-energy-like invariant of a graph, MATCH Commun. Math. Comput. Chem. 59, 355–372, 2008.
  • 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.
  • Liu, M. H. and Liu, B. L. The signless Laplacian spread, Linear Algebra Appl. 432 (2-3), –514, 2010.
  • 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.
  • Marshall, A. W. and Olkin, I. Inequalities, Theory of Majorization and its Applications (Academic Press, New York, 1979).
  • 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.
  • Pavlovi´c, L. Maximal value of the zeroth-order Randi´c index, Discrete Appl. Math. 127, –626, 2003.
  • 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.
  • 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.
  • Zhou, B. On sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra Appl. , 2239–2246, 2008.
  • Zhou, B. On sum of powers of Laplacian eigenvalues and Laplacian Estrada index of graphs, MATCH Commun. Math. Comput. Chem. 62, 611–619, 2009.
There are 24 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

Muhuo Liu This is me

 bolian Liu This is me

Publication Date April 1, 2012
Published in Issue Year 2012 Volume: 41 Issue: 4

Cite

APA Liu, M., & Liu, . (2012). On Sum of Powers of the Signless Laplacian Eigenvalues of Graphs  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics, 41(4), 527-536.
AMA Liu M, Liu . On Sum of Powers of the Signless Laplacian Eigenvalues of Graphs  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. April 2012;41(4):527-536.
Chicago Liu, Muhuo, and  bolian Liu. “On Sum of Powers of the Signless Laplacian Eigenvalues of Graphs  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 41, no. 4 (April 2012): 527-36.
EndNote Liu M, Liu  (April 1, 2012) On Sum of Powers of the Signless Laplacian Eigenvalues of Graphs  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics 41 4 527–536.
IEEE M. Liu and  . Liu, “On Sum of Powers of the Signless Laplacian Eigenvalues of Graphs  ABSTRACT  |  FULL TEXT ”, Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 4, pp. 527–536, 2012.
ISNAD Liu, Muhuo - Liu, bolian. “On Sum of Powers of the Signless Laplacian Eigenvalues of Graphs  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 41/4 (April 2012), 527-536.
JAMA Liu M, Liu . On Sum of Powers of the Signless Laplacian Eigenvalues of Graphs  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2012;41:527–536.
MLA Liu, Muhuo and  bolian Liu. “On Sum of Powers of the Signless Laplacian Eigenvalues of Graphs  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 4, 2012, pp. 527-36.
Vancouver Liu M, Liu . On Sum of Powers of the Signless Laplacian Eigenvalues of Graphs  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2012;41(4):527-36.