The first and second Zagreb indices of some graph operations

Discrete Applied Mathematics

Volumn 157, Issue 4, 2009, Pages 804-811

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

^a UNIVERSITY OF TEHRAN   (Iran)

^b UNIVERSITY OF KASHAN   (Iran)

^c INSTITUTE FOR RESEARCH IN FUNDAMENTAL SCIENCES IPM   (Iran)

Author keywords

C4 torus; C4 tube; Graph operations; q multi walled nanotorus; The first and second Zagreb indices

Indexed keywords

C4 TORUS; C4 TUBE; GRAPH OPERATIONS; Q-MULTI-WALLED NANOTORUS; THE FIRST AND SECOND ZAGREB INDICES;

EID: 59749104417     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2008.06.015     Document Type: Article

References (24)

1. Braun J., Kerber A., Meringer M., and Rucker C. Similarity of molecular descriptors: the equivalence of Zagreb indices and walk counts. MATCH Commun. Math. Comput. Chem. 54 (2005) 163-176
2. Diudea M.V., Gutman I., and Jantschi L. Molecular Topology (2001), Huntington, NY
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., Klavzar S., and Zigert P. Wiener index of hexagonal systems. Acta Appl. Math. 72 (2002) 247-294
5. Graovac A., and Pisanski T. On the Wiener index of a graph. J. Math. Chem. 8 (1991) 53-62
6. Gutman I., and Trinajstic N. Graph theory and molecular orbitals, Total πelectron energy of alternant hydrocarbons. Chem. Phys. Lett. 17 (1972) 535-538
7. Gutman I., and Das K.C. The first Zagreb index 30 years after. MATCH Commun. Math. Comput. Chem. 50 (2004) 83-92
8. Imrich W., and Klavzar S. Product Graphs: Structure and Recognition (2000), John Wiley & Sons, New York, USA
9. Khadikar P.V. On a novel structural descriptor PI. Natl. Acad. Sci. Lett. 23 (2000) 113-118
10. 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
11. Khalifeh M.H., Yousefi-Azari H., and Ashrafi A.R. Vertex and edge PI indices of Cartesian product graphs. Discrete Appl. Math. 156 (2008) 1780-1789
12. 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)
13. Khalifeh M.H., Yousefi-Azari H., and Ashrafi A.R. The Hyper-Wiener index of graph operations. Comput. Math. Appl. 56 (2008) 1402-1407
14. M.H. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, S.G. Wagner, Some new results on distance-based graph invariants, European J. Combin. (in press)
15. Klavzar S., Rajapakse A., and Gutman I. The Szeged and the Wiener index of graphs. Appl. Math. Lett. 9 (1996) 45-49
16. Nikolic S., Kovacevic G., Milicevic A., and Trinajstic N. The Zagreb indices 30 years after. Croat. Chem. Acta 76 (2003) 113-124
17. Sagan B.E., Yeh Y.-N., and Zhang P. The Wiener polynomial of a graph. Int. J. Quantum. Chem. 60 5 (1996) 959-969
18. Trinajstic N. Chemical Graph Theory (1992), CRC Press, Boca Raton, FL
19. Wiener H. Structural determination of the paraffin boiling points. J. Am. Chem. Soc. 69 (1947) 17-20
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. H. Yousefi-Azari, A.R. Ashrafi, Padmakar-Ivan index of q-multi-walled carbon nanotubes and nanotori, J. Comput. Theor. Nanosci. (in press)
22. Zhou B., and Gutman I. Relations between Wiener, hyper-Wiener and Zagreb indices. Chem. Phys. Lett. 394 (2004) 93-95
23. Zhou B. Zagreb indices. MATCH Commun. Math. Comput. Chem. 52 (2004) 113-118
24. Zhou B., and Gutman I. Further properties of Zagreb indices. MATCH Commun. Math. Comput. Chem. 54 (2005) 233-239