Degree Kirchhoff index of unicyclic graphs

Match

Volumn 69, Issue 3, 2013, Pages 629-648

  Feng, Lihua ^a,b   Gutman, Ivan ^c   Yu, Guihai ^a,b  

^a CENTRAL SOUTH UNIVERSITY   (China)

^b CHONGQING NORMAL UNIVERSITY   (China)

^c UNIVERSITY OF KRAGUJEVAC   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84898014903     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (47)

1. V. Andova, D. Dimitrov, J. Fink, R. Škrekovski, Bounds on Gutman index, MATCH Commun. Math. Comput. Chem. 67 (2012) 515-524.
2. R. B. Bapat, I. Gutman, W. Xiao, A simple method for computing resistance distance, Z. Naturforsch. 58a (2003) 494-498.
3. 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.
4. O. Bucicovschi, S. M. Cioabǎ, The minimum degree distance of graphs of given order and size, Discr. Appl. Math. 156 (2008) 3518-3521.
5. H. Chen, F. Zhang, Resistance distance and the normalized Laplacian spectrum, Discr. Appl. Math. 155 (2007) 654-661.
6. S. B. Chen, W. J. Liu, Extremal modified Schultz index of bicyclic graphs, MATCH Commun. Math. Comput. Chem. 64 (2010) 767-782.
7. F. R. K. Chung, Spectral Graph Theory, Am. Math. Soc., Providence, 1997.
8. P. Dankelmann, I. Gutman, S. Mukwembi, H. C. Swart, On the degree distance of a graph, Discr. Appl. Math. 157 (2009) 2773-2777.
9. P. Dankelmann, I. Gutman, S. Mukwembi, H. C. Swart, The edge-Wiener index of a graph, Discr. Math. 309 (2009) 3452-3457.
10. H. Deng, The Schultz molecular topological index of polyhex nanotubes, MATCH Commun. Math. Comput. Chem. 57 (2007) 677-684.
11. H. Deng, On the minimum Kirchhoff index of graphs with a given number of cut edges, MATCH Commun. Math. Comput. Chem. 63 (2010) 171-180.
12. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math. 66 (2001) 211-249.
13. A. A. Dobrynin, A. A. Kochetova, Degree distance of a graph: A degree analogue of the Wiener index, J. Chem. Inf. Comput. Sci. 34 (1994) 1082-1086.
14. T. Došlić, B. Furtula, A. Graovac, I. Gutman, S. Moradi, Z. Yarahmadi, On vertex-degree-based molecular structure descriptors, MATCH Commun. Math. Comput. Chem. 66 (2011) 613-626.
15. L. H. Feng, W. L. Liu, The maximal Gutman index of bicyclic graphs, MATCH Commun. Math. Comput. Chem. 66 (2011) 699-708.
16. R. Grone, R. Merris, The Laplacian spectrum of a graph II, SIAM J. Discr. Math. 7 (1994) 221-229.
17. R. Grone, R. Merris, V. S. Sunder, The Laplacian spectrum of a graph, SIAM J. Matrix Anal. Appl. 11 (1990) 218-238.
18. Q. Guo, H. Deng, D. Chen, The extremal Kirchhoff index of a class of unicyclic graphs, MATCH Commun. Math. Comput. Chem. 61 (2009) 713-722.
19. I. Gutman, Selected properties of the Schultz molecular topological index, J. Chem. Inf. Comput. Sci. 34 (1994) 1087-1089.
20. I. Gutman, K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004) 83-92.
21. I. Gutman, B. Furtula (Eds.), Distance in Molecular Graphs-Theory, Univ. Kragujevac, Kragujevac, 2012.
22. I. Gutman, B. Furtula (Eds.), Distance in Molecular Graphs-Applications, Univ. Kragujevac, Kragujevac, 2012.
23. I. Gutman, B. Mohar, The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996) 982-985.
24. A. Ilić, S. Klavžar, D. Stevanović, Calculating the degree distance of partial Hamming graphs, MATCH Commun. Math. Comput. Chem. 63 (2010) 411-424.
25. A. Ilić, D. Stevanović, L. Feng, G. Yu, P. Dankelmann, Degree distance of unicyclic and bicyclic graphs, Discr. Appl. Math. 159 (2011) 779-788.
26. D. J. Klein, Graph geometry, graph metrics, and Wiener, MATCH Commun. Math. Comput. Chem. 35 (1997) 7-27.
27. D. J. Klein, Z. Mihalić, D. Plavšić, N. Trinajstić, Molecular topological index: A relation with the Wiener index, J. Chem. Inf. Comput. Sci. 32 (1992) 304-305.
28. D. J. Klein, M. Randić, Resistance distance, J. Math. Chem. 12 (1993) 81-95.
29. M. Knor, P. Potočnik, R. Škrekovski, Relationship between edge-Wiener index and Gutman index of a graph, Appl. Math. Letters, to appear.
30. B. Mohar, The Laplacian spectrum of graphs, in: Y. Alavi, G. Chartrand, O. R. Oellermann, A. J. Schwenk (Eds.), Graph Theory, Combinatorics, and Applications, Wiley, New York, 1991, pp. 871-898.
31. J. Palacios, J. M. Renom, Another look at the degree Kirchhoff index, Int. J. Quantum Chem. 111 (2011) 3453-3455.
32. H. P. Schultz, Topological organic chemistry. 1. Graph theory and topological indices of alkanes, J. Chem. Inf. Comput. Sci. 29 (1989) 227-228.
33. R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000.
34. R. Todeschini, V. Consonni, Molecular Descriptors for Chemoinformatics, Wiley-VCH, Weinheim, 2009.
35. A. I. Tomescu, Unicyclic and bicyclic graphs having minimum degree distance, Discr. Appl. Math. 156 (2008) 125-130.
36. I. Tomescu, Some extremal properties of the degree distance of a graph, Discr. Appl. Math. 98 (1999) 159-163.
37. I. Tomescu, Properties of connected graphs having minimum degree distance, Discr. Math. 309 (2009) 2745-2748.
38. H. Wang, H. Hua, D. Wang, Cacti with minimum, second-minimum, and third-minimum Kirchhoff indices, Math. Commun. 15 (2010) 347-358.
39. W. Xiao, I. Gutman, Resistance distance and Laplacian spectrum, Theor. Chem. Acc. 110 (2003) 284-289.
40. W. Xiao, I. Gutman, On resistance matrices, MATCH Commun. Math. Comput. Chem. 49 (2003) 67-81.
41. W. Xiao, I. Gutman, Relations between resistance and Laplacian matrices and their applications, MATCH Commun. Math. Comput. Chem. 51 (2004) 119-127.
42. Y. J. Yang, X. Y. Jiang, Unicyclic graphs with extremal Kirchhoff index, MATCH Commun. Math. Comput. Chem. 60 (2008) 107-120.
43. G. Yu, L. Feng, On the Wiener index of unicyclic graphs with given girth, Ars Comb. 94 (2010) 361-369.
44. H. Yuan, C. An, The unicyclic graphs with maximum degree distance, J. Math. Study 39 (2006) 18-24.
45. W. Zhang, H. Deng, The second maximal and minimal Kirchhoff indices of unicyclic graphs, MATCH Commun. Math. Comput. Chem. 61 (2009) 683-695.
46. B. Zhou, Bounds for the Schultz molecular topological index, MATCH Commun. Math. Comput. Chem. 56 (2006) 189-194.
47. B. Zhou, N. Trinajstić, The Kirchhoff index and the matching number, Int. J. Quantum Chem. 109 (2009) 2978-2981.