Generalizations of Wiener Polarity Index and Terminal Wiener Index

Graphs and Combinatorics

Volumn 29, Issue 5, 2013, Pages 1403-1416

  Ilić, Aleksandar ^a   Ilić, Milovan ^b  

^a UNIVERSITY OF NI   (Serbia)

^b Metropolitan University   (Serbia)

Author keywords

Distance in graphs; Graph algorithm; Partial cube; Terminal Wiener index; Wiener index; Wiener polarity index

Indexed keywords

EID: 84882927771     PISSN: 09110119     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00373-012-1215-6     Document Type: Article

References (27)

1. Chepoi V., Klavžar S.: The Wiener index and the Szeged index of benzenoid systems in linear time. J. Chem. Inf. Comput. Sci. 37, 752-755 (1997).
2. Cormen T. H., Leiserson C. E., Rivest R. L., Stein C. (2001) Introduction to Algorithms, 2nd edn. MIT Press, Cambridge.
3. Dankelmann P., Gutman I., Mukwembi S., Swart H. C.: The edge-Wiener index of a graph. Discret. Math. 309, 3452-3457 (2009).
4. Deng H.: On the extremal Wiener polarity index of chemical trees. MATCH Commun. Math. Comput. Chem. 60, 305-314 (2011).
5. Deng H., Xiao H., Tang F.: The maximum Wiener polarity index of trees with k pendants. Appl. Math. Lett. 23, 710-715 (2010).
6. Deng H., Xiao H., Tang F.: On the extremal Wiener polarity index of trees with a given diameter. MATCH Commun. Math. Comput. Chem. 63, 257-264 (2010).
7. Deng, X., Zhang, J.: Equiseparability on terminal Wiener index. In: Goldberg, A. V., Zhou, Y. (eds.) Algorithmic Aspects in Information and Management, pp. 166-174. Springer, Berlin (2009).
8. Du W., Li X., Shi Y.: Algorithms and extremal problem on Wiener polarity index. MATCH Commun. Math. Comput. Chem. 62, 235-244 (2009).
9. Dobrynin A. A., Entringer R. C., Gutman I.: Wiener index of trees: theory and applications. Acta Appl. Math. 66, 211-249 (2001).
10. Gutman I., Furtula B., Petrović M.: Terminal Wiener index. J. Math. Chem. 46, 522-531 (2009).
11. Gutman I., Polansky O. E.: Mathematical Concepts in Organic Chemistry. Springer, Berlin (1988).
12. Gutman, I., Zhang, Y., Dehmer, M., Ilić, A.: Altenburg, Wiener, and Hosoya polynomials. In: Gutman, I., Furtula, B. (eds.) Distance in Molecular Graphs-Theory, pp. 49-70. Univerity of Kragujevac, Kragujevac (2012).
13. Hosoya, H.: Mathematical and chemical analysis of Wiener's polarity number. In: Rouvray, D. H., King, R. B. (eds.) Topology in Chemistry-Discrete Mathematics of Molecules. Horwood, Chichester (2002).
14. Hosoya H.: On some counting polynomials in chemistry. Discret. Appl. Math. 19, 239-257 (1988).
15. Ilić A., Stevanović D.: On Comparing Zagreb Indices. MATCH Commun. Math. Comput. Chem. 62, 681-687 (2009).
16. Ilić A., Ilić A., Stevanović D.: On the Wiener index and Laplacian coefficients of graphs with given diameter or radius. MATCH Commun. Math. Comput. Chem. 63, 91-100 (2010).
17. Ilić A., Klavžar S., Stevanović D.: Calculating the degree distance of partial Hamming graphs. MATCH Commun. Math. Comput. Chem. 63, 411-424 (2010).
18. Imrich W., Klavžar S.: Product Graphs: Structure and Recognition. Wiley, New York (2000).
19. Klavžar S.: Bird's eye view of the cut method and a survey of its applications in chemical graph theory. MATCH Commun. Math. Comput. Chem. 60, 255-274 (2008).
20. Klavžar S., Gutman I.: Wiener number of vertex-weighted graphs and a chemical application. Discret. Appl. Math. 80, 73-81 (1997).
21. Liu B., Hou H., Huang Y.: On the Wiener polarity index of trees with maximum degree or given number of leaves. Comp. Math. Appl. 60, 2053-2057 (2010).
22. Nikolić S., Kovačević G., Milićević A., Trinajstić N.: The Zagreb indices 30 years after. Croat. Chem. Acta 76, 113-124 (2003).
23. Sagan B. E., Yeh Y. N., Zhang P.: The Wiener polynomial of a graph. Int. J. Quantum Chem. 60, 959-969 (1996).
24. Székely, L. A., Wang, H., Wu, T.: The sum of the distances between the leaves of a tree and the 'semi-regular' property. Discret. Math. 311, 1197-1203 (2011). doi: 10. 1016/j. disc. 2010. 06. 005.
25. Todeschini R., Consonni V.: Handbook of Molecular Descriptors. Wiley, Weinheim (2000).
26. Winkler P.: Isometric embeddings in products of complete graphs. Discret. Appl. Math. 7, 221-225 (1984).
27. Zaretskii K. A.: Construction of trees using the distances between pendent vertices. Uspekhi Math. Nauk. 20, 90-92 (1965).