Have a personal or library account? Click to login
Computing Laplacian energy, Laplacian-energy-like invariant and Kirchhoff index of graphs Cover

Computing Laplacian energy, Laplacian-energy-like invariant and Kirchhoff index of graphs

By: S. Bhatnagar,  Merajuddin and  S. Pirzada  
Open Access
|Feb 2023

References

  1. [1] K.C. Das, A sharp upper bound for the number of spanning trees of a graph, Graphs Comb. 23 (2007) 625–632. ⇒188, 19310.1007/s00373-007-0758-4
  2. [2] B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015) 1184–1190. ⇒18610.1007/s10910-015-0480-z
  3. [3] I. Gutman, N. Trinajstic, Graph Theory and Molecular Orbitals, Total π-electron energy of alternate hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538. ⇒18610.1016/0009-2614(72)85099-1
  4. [4] I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forschungszenturm Graz 103 (1978) 1–22. ⇒186
  5. [5] I. Gutman, B. Zhou, Laplacian energy of a graph, Linear Algebra Appl. 414 (2006) 29–37. ⇒18710.1016/j.laa.2005.09.008
  6. [6] I. Gutman, B. Mohar, The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996) 982–985. ⇒18810.1021/ci960007t
  7. [7] T. Hayashi, On some inequalities, Rend. Circ. Mat. Palermo 44 (1920) 336–340. ⇒19110.1007/BF03014605
  8. [8] P. Henrici, Two remarks on Kantorovich inequality, Amer. Math. Monthly 68(9) (1961) 904–906. ⇒19110.2307/2311698
  9. [9] D.J. Klein, M. Randic, Resistence distance, J. Math. Chem. 12 (1993) 81–95. ⇒18710.1007/BF01164627
  10. [10] J. Liu, B.A. Liu, A Laplacian-Energy-like invariant of a graph, MATCH Commun. Math. Comput. Chem. 59 (2008) 355–372. ⇒187, 188
  11. [11] B. Liu, Z.Y. Liu, A Survey on the Laplacian-energy-like invariant, MATCH Commun. Math. Comput. Chem. 66 (2011) 713–730. ⇒187
  12. [12] E.I. Milovanovic, I. Z. Milovanovic, M. M. Matejic, On relation between Kirchhoff index and Laplacian-energy-like invariant of graphs, Math. Int. Res. 2 (2017) 141–154. ⇒187
  13. [13] I. Milovanovic, E. Milovanovic, E. Glogic, M. Matejic, On Kirchhoff index, Laplacian energy and their relation, MATCH Commun. Math. Comput. Chem. 81 (2019) 405–418. ⇒187
  14. [14] P. Milosevic, E. Milovanovic, M. Matejic, I. Milovanovic, On relations between Kirchhoff index, Laplacian energy, Laplacian–energy–like invariant and degree deviation of graphs, Filomat 34(2020) 1025—1033. ⇒187, 19610.2298/FIL2003025M
  15. [15] S. Pirzada, An Introduction to Graph Theory, Universities Press, Hyderabad, India, 2012. ⇒186
  16. [16] S. Pirzada, H.A. Ganie, On Laplacian-Energy-like invariant and Incidence energy, Trans. Comb. 4(3) (2015) 25–35. ⇒
  17. [17] S. Pirzada, H.A. Ganie, I. Gutman, On Laplacian-Energy-like invariant and Kirchhoff Index, MATCH Commun. Math. Comput. Chem. 73 (2015) 41–60. ⇒187
  18. [18] S. Pirzada, H. A. Ganie, I. Gutman, Comparison between Laplacian-energy-like invariant and the Kirchhoff index, Elec. J. Lin. Algebra 31 (2016) 27–41. ⇒18710.13001/1081-3810.2961
  19. [19] J. Radon, Theorie und Anwendungen der absolut Additiven Mengenfunktionnem, Sitzungsber Acad. Wissen, Wien 122 (1913) 1295–1438. ⇒193
  20. [20] J. Szőkefalvi Nagy, Uber algebraische Gleichungenmit lauter reellen Wurzeln, Jahresbericht der deutschen Mathematiker Vereingung 27 (1918) 37–43. ⇒188
  21. [21] H. Wiener, Structural determination of paraffin boilling points, J. Amer. Chem. Soc. 69 (1947) 17–20. ⇒18710.1021/ja01193a00520291038
  22. [22] H.Y. Zhu, D.J. Klein, I. Lukovits, Extensions of the Wiener numbers, J. Chem. Inform. Comput. Sci. 36(3) (1996) 420–428. ⇒18810.1021/ci950116s
Language: English
Page range: 185 - 198
Submitted on: Oct 1, 2022
|
Accepted on: Nov 6, 2022
|
Published on: Feb 4, 2023
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2023 S. Bhatnagar, Merajuddin, S. Pirzada, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.