The hyper-Wiener index of graph operations

Computers and Mathematics with Applications

Volumn 56, Issue 5, 2008, Pages 1402-1407

  Khalifeh, M H ^a   Yousefi Azari, H ^a   Ashrafi, A R ^b  

^a UNIVERSITY OF TEHRAN   (Iran)

^b UNIVERSITY OF KASHAN   (Iran)

Author keywords

C4 nanotorus; C4 nanotube; Graph operations; Hyper Wiener index; q multi walled nanotube

Indexed keywords

MICROFLUIDICS;

GRAPH G; SHORTEST PATH (SP); WIENER INDICES;

GRAPH THEORY;

EID: 46449098008     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2008.03.003     Document Type: Article

References (30)

1. Dobrynin A.A., Entringer R., and Gutman I. Wiener index of trees: Theory and applications. Acta Appl. Math. 66 (2001) 211-249
2. Dobrynin A.A., Gutman I., Klavzar S., and Zigert P. Wiener index of hexagonal systems. Acta Appl. Math. 72 (2002) 247-294
3. In: Gutman I., Klavzar S., and Mohar B. (Eds). Fifty years of the Wiener index. MATCH Commun. Math. Comput. Chem. 35 (1997) 1259
4. In: Gutman I., Klavzar S., and Mohar B. (Eds). Fiftieth anniversary of the Wiener index. Discrete Appl. Math. 80 1 (1997) 1113
5. Wiener H. Structural determination of the paraffin boiling points. J. Am. Chem. Soc. 69 (1947) 17-20
6. Klein D.J., Lukovits I., and Gutman I. On the definition of the hyper-Wiener index for cycle-containing structures. J. Chem. Inf. Comput. Sci. 35 (1995) 50-52
7. Cash G.G. Relationship between the Hosoya polynomial and the Hyper-Wiener index. Appl. Math. Lett. 15 (2002) 893-895
8. Cash G.G. Polynomial expressions for the hyper-Wiener index of extended hydrocarbon networks. Comput. Chem. 25 (2001) 577-582
9. Gutman I. Relation between hyper-Wiener and Wiener index. Chem. Phys. Lett. 364 (2002) 352-356
10. Klavzar S., Zigert P., and Gutman I. An algorithm for the calculation of the hyper-Wiener index of benzenoid hydrocarbons. Comput. Chem. 24 (2000) 229-233
11. Klavzar S., and Gutman I. A theorem on Wiener-type invariants for isometric subgraphs of hypercubes. Appl. Math. Lett. 19 (2006) 1129-1133
12. Li X., and Jalbout A.F. Bond order weighted hyper-Wiener index. J. Mol. Structure (Theochem) 634 (2003) 121-125
13. Zhou B., and Gutman I. Relations between Wiener, hyper-Wiener and Zagreb indices. Chem. Phys. Lett. 394 (2004) 93-95
14. Graovac A., and Pisanski T. On the Wiener index of a graph. J. Math. Chem. 8 (1991) 53-62
15. Sagan B.E., Yeh Y.-N., and Zhang P. The Wiener polynomial of a graph. Int. J. Quant. Chem. 60 5 (1996) 959-969
16. Klavzar S., Rajapakse A., and Gutman I. The Szeged and the Wiener index of graphs. Appl. Math. Lett. 9 (1996) 45-49
17. Khalifeh M.H., Yousefi-Azari H., and Ashrafi A.R. Vertex and edge PI indices of cartesian product graphs. Discrete Appl. Math. (2007) 10.1016/j.dam.2007.08.041
18. M.H. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, I. Gutman, The Edge Szeged Index of Product Graphs, Croat. Chem Acta, 81 (2) (2008) (in press)
19. M.H. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, The first and second zagreb indices of graph operations (in press)
20. Yousefi-Azari H., Manoochehrian B., and Ashrafi A.R. The PI index of product graphs. Appl. Math. Lett. 21 6 (2008) 624-627
21. Imrich W., and Klavzar S. Product Graphs: Structure and Recognition (2000), Wiley, New York, USA
22. Khalifeh M.H., Yousefi-Azari H., and Ashrafi A.R. A matrix method for computing szeged and vertex pi indices of join and composition of graphs. Linear Algebra Appl. (2008) 10.1016/j.laa.2008.01.015
23. Khadikar P.V. On a novel structural descriptor PI. Nat. Acad. Sci. Lett. 23 (2000) 113-118
24. Ashrafi A.R., and Loghman A. PI index of zig-zag polyhex nanotubes. MATCH Commun. Math. Comput. Chem. 55 2 (2006) 447-452
25. M.V. Diudea, I. Gutman, L. Jantschi, Molecular Topology, Huntington, NY, 2001
26. Trinajstic N. Chemical Graph Theory (1992), CRC Press, Boca Raton, FL
27. H. Yousefi-Azari, A.R. Ashrafi, Padmakar-Ivan Index of q-Multi-walled Carbon Nanotubes and Nanotori, J. Comput. Theor. Nanosci. (in press)
28. Gutman I. A property of the Wiener number and its modifications. Indian J. Chem. 36A (1997) 128-132
29. Yousefi S., and Ashrafi A.R. An Exact expression for the wiener index of a polyhex nanotorus. MATCH Commun. Math. Comput. Chem. 56 (2006) 169-178
30. S. Yousefi, H. Yousefi-Azari, A.R. Ashrafi, M.H. Khalifeh, Computing Distance Matrix and Related Topological Indices of a Polyhex Nanotorus (submitted for publication)