On resistance matrices

Match

Volumn , Issue 49, 2003, Pages 67-81

  Xiao, Wenjun ^a,b   Gutman, Ivan ^c  

^a XIAMEN UNIVERSITY   (China)

^b SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

^c UNIVERSITY OF KRAGUJEVAC   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC METHOD; ARTICLE; CALCULATION; ELECTRIC RESISTANCE; ELECTRICITY; SPECTRUM;

EID: 0345491468     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. D. J. Klein and M. Randić, Resistance distance, J. Math. Chem. 12 (1993) 81-95.
2. 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.
3. H. Y. Zhu, D. J. Klein and I. Lukovits, Extensions of the Wiener number, J. Chem. Inf. Comput. Sci. 36 (1996) 420-428.
4. I. Gutman and B. Mohar, The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996) 982-985.
5. D. J. Klein, Graph geometry, graph metrics, & Wiener, MATCH - Commun. Math. Comput. Chem. 35 (1997) 7-27.
6. D. J. Klein and H. Y. Zhu, Distances and volumina for graphs, J. Math. Chem. 23 (1998) 179-195.
7. I. Lukovits, S. Nikolić and N. Trinajstić, Resistance distance in regular graphs, Int. J. Quantum Chem. 71 (1999) 217-225.
8. D. J. Klein and O. Ivanciuc, Graph cyclicicty, excess conductance, and resistance deficit, J. Math. Chem. 30 (2001) 271-287.
9. J. L. Palacios, Resistance distance in graphs and random walks, Int. J. Quantum Chem. 81 (2001) 29-33.
10. J. L. Palacios, Closed-form formulas for Kirchhoff index, Int. J. Quantum Chem. 81 (2001) 135-140.
11. D. J. Klein, Resistance-distance sum rules, Croat. Chem. Acta 75 (2002) 633-649.
12. 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.
13. B. Mohar, The Laplacian spectrum of graphs, in: Y. Alavi, G. Chartrand, O. R. Ollermann and A. J. Schwenk (Eds.), Graph Theory, Combinatorics, and Applications, Wiley, New York, 1991, pp. 871-898.
14. R. Merris, Laplacian matrices of graphs: A survey, Lin. Algebra Appl. 197-198 (1994) 143-176.
15. N. Trinajstić, D. Babić, S. Nikolić, D. Plavšić, D. Amić and Z. Mihalić, The Laplacian matrix in chemistry, J. Chem. Inf. Comput. Sci. 34 (1994) 368-376.
16. 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), in press.
17. A. Ben-Israel and T. N. E. Greville, Generalized Inverses - Theory and Applications, Wiley, New York, 1974.
18. S. L. Campbell and C. D. Meyer, Generalized Inverses of Linear Transformations, Pitman, London, 1979.
19. D. M. Cvetković, M. Doob and H. Sachs, Spectra of Graphs - Theory and Application, Academic Press, New York, 1980.
20. F. R. K. Chung, Spectral Graph Theory, American Math. Soc., Providence, 1997.