Relations between resistance and laplacian matrices and their applications

Match

Volumn , Issue 51, 2004, Pages 119-127

  Xiao, Wenjun ^a   Gutman, Ivan ^b  

^a SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

^b UNIVERSITY OF KRAGUJEVAC   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ELECTRICITY; LAPLACIAN MATRIX; MATHEMATICAL ANALYSIS; MATHEMATICS; MOLECULE; RESISTANCE MATRIX;

EID: 9144237194     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. F. Buckley and F. Harary, Distance in Graphs, Addison-Wesley, Redwood, 1990.
2. B. Lučić, I. Lukovits, S. Nikolić and N. Trinajstic, Distance-related indexes in the quantitative structure-property relationship modeling, J. Chem. Inf. Comput. Sci. 41 (2001) 527-535.
3. A. A. Dobrynin, R. Entringer and I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math. 66 (2001) 211-249.
4. M. V. Diudea, B. Pãrv, P. E. John, O. Ursu and A. Graovac, Distance counting in tori, MATCH Commun. Math. Comput. Chem. 49 (2003) 23-36.
5. A. A. Dobrynin, On the Wiener index decomposition for catacondensed benzenoid graphs, Indian J. Chem. 42A (2003) 1270-1271.
6. A. A. Dobrynin, Wiener index decomposition based on vertex degrees of catacondensed benzenoid graphs, MATCH Commun. Math. Comput. Chem. 49 (2003) 37-46.
7. A. Graovac, M. Juvan, M. Petkovšek, A. Vesel and J. Žerovnik, The Szeged index of fasciagraphs, MATCH Commun. Math. Comput. Chem. 49 (2003) 47-66.
8. A. A. Dobrynin and L. S. Mel'nikov, Trees and their quadratic line graphs having the same Wiener index, MATCH Commun. Math. Comput. Chem. 50 (2004) 146-164.
9. M. Gorše and J. Žerovnik, A remark on modified Wiener indices, MATCH Commun. Math. Comput. Chem. 50 (2004) 109-116.
10. 8 nanotubes, MATCH Commun. Math. Comput. Chem. 50 (2004) 133-144.
11. D. Vukičević and A. Graovac, On modified Wiener indices of thorn graphs, MATCH Commun. Math. Comput. Chem. 50 (2004) 93-108.
12. H. B. Walikar, V. S. Shigehalli and H. S. Ramane, Bounds on the Wiener number of a graph, MATCH Commun. Math. Comput. Chem. 50 (2004) 117-132.
13. D. J. Klein and M. Randić, Resistance distance, J. Math. Chem. 12 (1993) 81-95.
14. D. Bonchev, A. T. Balaban, X. Liu and 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.
15. H. Y. Zhu, D. J. Klein and I. Lukovits, Extensions of the Wiener number, J. Chem. Inf. Comput. Sci. 36 (1996) 420-428.
16. I. Gutman and B. Mohar, The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996) 982-985.
17. D. J. Klein, Graph geometry, graph metrics, & Wiener, MATCH - Commun. Math. Comput. Chem. 35 (1997) 7-27.
18. R. B. Bapat, Resistance distance in graphs, Math. Student 68 (1999) 87-98.
19. I. Lukovits, S. Nikolić and N. Trinajstić, Resistance distance in regular graphs, Int. J. Quantum Chem. 71 (1999) 217-225.
20. D. J. Klein and O. Ivanciuc, Graph cyclicity, excess conductance, and resistance deficit, J. Math. Chem. 30 (2001) 271-287.
21. J. L. Palacios, Resistance distance in graphs and random walks, Int. J. Quantum Chem. 81 (2001) 29-33.
22. J. L. Palacios, Closed-form formulas for Kirchhoff index, Int. J. Quantum Chem. 81 (2001) 135-140.
23. D. J. Klein, Resistance-distance sum rules, Croat. Chem. Acta 75 (2002) 633-649.
24. D. Babić, D. J. Klein, I. Lukovits, S. Nikolić and N. Trinajstić, Resistance-distance matrix. A computational algorithm and its application, Int. J. Quantum Chem. 90 (2002) 161-176.
25. W. Xiao and I. Gutman, On resistance matrices, MATCH - Commun. Math. Comput. Chem. 49 (2003) 67-81.
26. R. B. Bapat, I. Gutman and W. Xiao, A simple method for computing resistance distance, Z. Naturforsch. 58a (2003) 494-498.
27. I. Gutman, D. Vidović and B. Furtula, Chemical applications of the Laplacian spectrum. VII. Studies of the Wiener and Kirchhoff indices, Indian J. Chem. 42A (2003) 1272-1278.
28. W. Xiao and I. Gutman, Resistance distance and Laplacian spectrum, Theor. Chem. Acc. 110 (2003), in press.
29. S. Seshu and M. B. Read, Linear Graphs and Electrical Networks, Addison-Wesley, Reading, 1961.
30. J. A. Edminster, Electric Circuits, McGraw-Hill, New York, 1965.
31. B. Bollobás, Modern Graph Theory, Springer-Verlag, New York, 1998, chapter 9.
32. A. Ben-Israel and T. N. E. Greville, Generalized Inverses - Theory and Applications, Wiley, New York, 1974.
33. S. L. Campbell and C. D. Meyer, Generalized Inverses of Linear Transformations, Pitman, London, 1979.
34. I. Gutman and W. Xiao, Generalized inverse of the Laplacian matrix and some applications, Bull. Acad. Serbe Sci. Arts (Cl. Math. Natur.), in press.