Branchings in trees and the calculation of the Wiener index of a tree

Match

Volumn 41, Issue , 2000, Pages 119-134

  Dobrynin, Andrey A ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

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EID: 0346364234     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. Wiener H. Structural determination of paraffin boiling points, J. Amer. Chem. Soc. 69 (1947) 17-20.
2. Hosoya H. Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn. 4 (1971) 2332-2339.
3. Trinajstić N. Chemical Graph Theory; CRC Press: Boca Raton, 1983; 2nd edition 1992.
4. Gutman I. and Polansky O. E. Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin, 1986.
5. Chemical Graph Theory - Introduction and Fundamentals; Bonchev, D; Rouvray, D. H., Eds.; Gordon & Breach: New York, 1991.
6. Bonchev D. and Trinajstić N. Information theory, distance matrix and molecular branching, J. Chem. Phys. 67 (1977) 4517-4533.
7. Rouvray D. H. Should we have designs on topological indices?, in: King, R. B. (ed.), Chemical Application of Topology and Graph Theory, Elsevier, Amsterdam, 1983, pp. 159-177.
8. Balaban A. T., Motoc I., Bonchev D. and Mekenyan O. Topological indices for structure-activity correlations. Topics Curr. Chem. 114 (1983) 21-55.
9. Rouvray D. H. Predicting chemistry from topology, Sci. Amer. 255 (9) (1986) 40-47.
10. Rouvray D. H. The modelling of chemical phenomena using topological indices, J. Comput. Chem. 8 (1987) 470-480.
11. Gutman I., Yeh Y. N., Lee S. L. and Luo Y. L. Some recent results in the theory of the Wiener number, Indian J. Chem. 32A (1993) 651-661.
12. Nikolić S., Trinajstić N. and Mihalić Z. The Wiener index: developments and applications, Croat. Chem. Acta 68 (1995) 105-129.
13. Gutman I. and Potgieter J. H. Wiener index and intermolecular forces, J. Serb. Chem. Soc. 62 (1997) 185-192.
14. Gutman I., Yeh Y. N., Lee S. L. and Chen J. C. Wiener numbers of dendrimers, Commun. Math. Chem. (MATCH) 30 (1994) 103-115.
15. Canfield E. R., Robinson R. W. and Rouvray D. H. Determination of the Wiener molecular branching index for the general tree, J. Comput. Chem. 6 (1985) 598-609.
16. Doyle J. K. and Graver J. E. Mean distance in a graph, Discrete Math. 7 (1977) 147-154.
17. Gutman I. Calculating the Wiener number: the Doyle-Graver method, J. Serb. Chem. Soc. 58 (1993) 745-750.
18. Dobrynin A. A. and Gutman I. On a graph invariant related to the sum of all distances in a graph, Publ. Inst. Math. (Beograd) 56 (1994) 18-22.
19. Klein D. J., Mihalić Z., Plavšić D. and Trinajstić N. Molecular topological index: a relation with the Wiener index, J. Chem. Inf. Comput. Sci. 32 (1992) 304-305.
20. Entringer R. C., Jackson D. E. and Snyder D. A. Distance in graphs, Czechoslovak Math. J. 26 (1976) 283-296.
21. Plesnik J. On the sum of all distances in a graph or digraph, J. Graph Theory 8 (1984) 1-21.
22. Polansky O. E. and Bonchev D. The Wiener number of graphs. I. General theory and changes due to some graph operations, Commun. Math. Chem. (MATCH) 21 (1986) 133-186.
23. Skorobogatov V. A. and Dobrynin A. A. Metric analysis of graphs, Commun. Math. Chem. (MATCH) 23 (1988) 105-151.
24. Mohar B. and Pisanski T. How to compute the Wiener index of a graph, J. Math. Chem. 2 (1988) 267-277.
25. Senn P. The computation of the distance matrix and the Wiener index for graphs of arbitrary complexity with weighted vertices and edges. Comput. Chem. 12 (1988) 219-227.
26. Polansky O. E. and Bonchev D. Theory of the Wiener number of graphs. II. Transfer graphs and some of their metric properties, Commun. Math. Chem. (MATCH) 25 (1990) 3-39.
27. Gutman I. and Rouvray D. H. A new theorem for the Wiener molecular branching index of trees with perfect matchings, Comput. Chem. 14 (1990) 29-32.
28. Buckley F. and Harary F. Distance in Graphs, Addison-Wesley, Redwood, 1990.
29. Graovac A. and Pisanski T. On the Wiener index of a graph, J. Math. Chem. 8 (1991) 53-62.
30. Mohar B., Babić D. and Trinajstić N. A novel definition of the Wiener index for trees, J. Chem. Inf. Comput. Sci. 33 (1993) 153-154.
31. Entringer R. C., Meir A., Moon J. W. and Székely L. A. On the Wiener index of trees from certain families, Australas. J. Combin. 10 (1994) 211-224.
32. John P. E. Calculation of the Wiener index for a simple polytree. Commun. Math. Chem. (MATCH) 31 (1994) 123-132.
33. Lukovits I. and Gutman I. Edge-decomposition of the Wiener number. Commun. Math. Chem. (MATCH) 31 (1994) 133-144.
34. Juvan M., Mohar B., Graovac A., Klavžar S. and Žerovnik J. Fast computation of the Wiener index of fasciagraphs and rotagraphs. J. Chem. Inf. Comput. Sci. 35 (1995) 834-840.
35. Entringer R. C. Distance in graphs: trees. J. Combin. Math. Combin. Comput. 24 (1997) 65-84.
36. Gutman I. Distance of thorny graphs, Publ. Inst. Math. (Beograd) 63 (1998) 31-36.
37. Dobrynin A. A. and Gutman I. The Wiener index for trees and graphs of hexagonal systems, Diskretn. Anal. Issled. Oper. Ser. 2 5(2) (1998) 34-60, in Russian.