On kirchhoff index and resistance-distance energy of a Graph

Match

Volumn 67, Issue 2, 2012, Pages 541-556

  Das, Kinkar Ch ^a   Gungor, A Dilek ^b   Çevik, A Sinan ^b  

^a Sungkyunkwan University   (South Korea)

^b SELCUK UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84858000814     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. W. Xiao, I. Gutman, Resistance distance and Laplacian spectrum, Theor. Chem. Ace. 110 (2003) 284-289.
2. W. Xiao, I. Gutman, On resistance matrices, MATCH Commun. Math. Comput. Chem. 49 (2003) 67-81.
3. D. J. Klein, Graph geometry, graph metrics, & Wiener, MATCH Commun. Math. Comput. Chem. 35 (1997) 7-27.
4. H. Chen, F. Zhang, Resistance distance and the normalized Laplacian spectrum, Discr. Appl. Math. 155 (2007) 654-661.
5. F. Buckley, F. Harary, Distance in Graphs, Addison-Wesley, Redwood, 1990.
6. D. J. Klein, M. Randic, Resistance distance, J. Math. Chem. 12 (1993) 81-95.
7. D. Bonchev, A. T. Balaban, X. Liu, D. J. Klein, Molecular cyclicity and centricity of polycyclic graphs. I. Cyclicity based on resistance distances or reciprocal distances, Int. J. Quantum Chem. 50 (1994) 1-20.
8. B. Zhou, N. TWnajstic, A note on Kirchhoff index, Chem. Phys. Lett. 455 (2008) 120-123.
9. R. Merris, Laplacian matrices of graphs: A survey, Lin. Algebra Appl. 197-198 (1994) 143-176.
10. J. S. Li, Y. L. Pan, A note on the second largest eigenvalue of the Laplacian matrix of a graph, Lin. Multilin. Algebra 48 (2000) 117-121.
11. M. Fiedler, Algebraic connectivity of graphs, Czech. Math. J. 37 (1987) 660-670.
12. K. C. Das, A sharp upper bound for the number of spanning trees of a graph, Graphs Combin. 23 (2007) 625-632.
13. I. Gutman, N. Trinajstic, Graph theory and molecular orbitals. Total jr-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535-538.
14. K. C. Das, Maximizing the sum of the squares of the degrees of a graph, Discr. Math. 285 (2004) 57-66.
15. I. Gutman, K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004) 83-92.
16. D. Cvetkovic, P. Rowlinson, S. K. Simic, Introduction to the Theory of Graph Spectra, Cambridge Univ. Press, Cambridge, 2010.
17. A. Graovac, I. Gutman, N. Trinajstic, Topological Approach to the Chemistry of Conjugated Molecules, Springer-Verlag, Berlin, 1977.
18. D. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs - Theory and Application, Academic Press, New York, 1980.
19. I. Gutman, The energy of a graph: Old and new results, in: A. Betten, A. Kohnert, R. Laue, A. Wassermann (Eds.), Algebraic Combinatorics and Applications, Springer-Verlag, Berlin, 2001.
20. B. Zhou, I. Gutman, On Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 57 (2007) 211-220.
21. G. Indulal, I. Gutman, A. Vijayakumar, On distance energy of graphs, MATCH Commun. Math. Comput. Chem. 60 (2008) 461-472.
22. V. Consonni, R. Todeschini, New spectral indices for molecule description, MATCH Commun. Math. Comput. Chem. 60 (2008) 3-14.
23. V. Nikiforov, The energy of graphs and matrices, J. Math. Anal. Appl. 326 (2007) 1472-1475.
24. M. R. Jooyandeh, D. Kiani, M. Mirzakhah, Incidence energy of a graph, MATCH Commun. Math. Comput. Chem. 62 (2009) 561-572.
25. R. A. Horn, C. R. Johnson, Matrix Analysis, Cambridge Univ. Press, New York, 1985.
26. B. Zhou, I. Gutman, T. Aleksic, A note on the Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 60 (2008) 441-446.
27. M. Edelberg, M. R. Garey, R. L. Graham, On distance matrix of a tree, Discr. Math. 14 (1976) 23-39.
28. R. B. Bapat, Resistance matrix and q-Laplacian of a unicyclic graph, Ramanujan Math. Soc. Lect. Notes Ser. 7 (2008) 63-72.