Reciprocal complementary Wiener numbers of trees, unicyclic graphs and bicyclic graphs

Discrete Applied Mathematics

Volumn 157, Issue 14, 2009, Pages 3046-3054

  Cai, Xiaochun ^a   Zhou, Bo ^a  

^a SOUTH CHINA NORMAL UNIVERSITY   (China)

Author keywords

Bicyclic graphs; Diameter; Distance; Reciprocal complementary Wiener number; Trees; Unicyclic graphs; Wiener number

Indexed keywords

BICYCLIC GRAPHS; DIAMETER; DISTANCE; RECIPROCAL COMPLEMENTARY WIENER NUMBER; TREES; UNICYCLIC GRAPHS; WIENER NUMBER;

NUMBER THEORY;

GRAPH THEORY;

EID: 67949104953     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2009.05.001     Document Type: Article

References (23)

1. Bonchev D. Information Theoretic Indices for Characterization of Chemical Structures (1983), Research Studies Press, Wiley, Chichester pp. 71-74
2. In: Devillers J., and Balaban A.T. (Eds). Topological Indices and Related Descriptors in QSAR and QSPR (1999), Gordon and Breach, The Netherlands
3. Dobrynin A.A., Entringer R., and Gutman I. Wiener index of trees: Theory and applications. Acta Appl. Math. 66 (2001) 211-249
4. Dobrynin A.A., Gutman I., Klavžar S., and Žigert P. Wiener index of hexagonal systems. Acta Appl. Math. 72 (2002) 247-294
5. Fifty years of the Wiener index. In: Gutman I., Klavžar S., and Mohar B. (Eds). MATCH Commun. Math. Comput. Chem. 35 (1997) 1-259
6. Fiftieth anniversary of the Wiener index. In: Gutman I., Klavžar S., and Mohar B. (Eds). Discrete Appl. Math. 80 (1997) 1-113
7. Gutman I., and Polansky O.E. Mathematical Concepts in Organic Chemistry (1986), Springer-Verlag, Berlin
8. Hosoya H. Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull. Chem. Soc. Japan 44 (1971) 2332-2339
9. Ivanciuc O. Graph theory in chemistry. In: Gasteiger J. (Ed). Handbook of Chemoinformatics (2003), Wiley-VCH, Weinheim 103-138
10. Ivanciuc O. Topological indices. In: Gasteiger J. (Ed). Handbook of Chemoinformatics (2003), Wiley-VCH, Weinheim 981-1003
11. Ivanciuc O. QSAR comparative study of Wiener descriptors for weighted molecular graphs. J. Chem. Inf. Comput. Sci. 40 (2000) 1412-1422
12. Ivanciuc O., Ivanciuc T., and Balaban A.T. The complementary distance matrix, a new molecular graph metric. ACH-Models Chem. 137 (2000) 57-82
13. Ivanciuc O., Ivanciuc T., and Balaban A.T. Quantitative structure-property relationship evaluation of structural descriptors derived from the distance and reverse Wiener matrices. Internet Electron. J. Mol. Des. 1 (2002) 467-487
14. Ivanciuc O., Ivanciuc T., and Balaban A.T. Vertex-and edge-weighted molecular graphs and derived structural descriptors. In: Devillers J., and Balaban A.T. (Eds). Topological Indices and Related Descriptors in QSAR and QSPR (1999), Gordon and Breach, The Netherlands 169-220
15. Janežić D., Miličević A., Nikolić S., and Trinajstić N. Graph-Theoretical Matrices in Chemistry (2007), University of Kragujevac, Kragujevac
16. Nikolić S., Trinajstić N., and Mihalić M. The Wiener index: Development and applications. Croat. Chem. Acta 68 (1995) 105-128
17. Rada J. Variation of the Wiener index under tree transformations. Discrete Appl. Math. 148 (2005) 135-146
18. Todeschini R., and Consonni V. Handbook of Molecular Descriptors (2000), Wiley-VCH, Weinheim
19. Trinajstić N. Chemical Graph Theory. 2nd revised edn (1992), CRC press, Boca Raton
20. Wiener H. Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69 (1947) 17-20
21. Yousefi S., and Ashrafi A.R. An exact expression for the Wiener index of polyhex nanotorus. MATCH Commun. Math. Comput. Chem. 56 (2006) 169-178
22. 8(R) nanotorus. J. Math. Chem. 42 (2007) 1031-1039
23. Zhou B., Cai X., and Trinajstić N. On reciprocal complementary Wiener number. Discrete Appl. Math. 157 (2009) 1628-1633