Zagreb Polynomials of Certain Families of Dendrimer Nanostars
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Abstract
Let G be a simple connected graph with vertex set V(G) and edge set E(G). The first, second and third Zagreb polynomials of G are defined as , and A dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, the first, second and third Zagreb polynomials of three types of dendrimers are computed.
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References
1. M.B. Ahmadi, M. Sadeghimehr, Second order
connectivity index of an infinite class of dendrimer
nanostars, Dig. J. Nanomater. Bios. 4 (2009), 639-
643.
2. S. Alikhani, M.A. Iranmanesh, Chromatic
polynomials of some dendrimers, J. Comput. Theor.
Nanosci. 7 (2010), 2314-2316.
3. A. Astaneh-Asl, G. Fath-Tabar, Computing the
first and third Zagreb polynomials of Cartesian
product of graphs, Iranian J. Math. Chem 2(2) (2011),
73-78.
4. N.E. Arif, R. Hasni, S. Alikhani, Chromatic
polynomials of certain families of dendrimer
nanostars, Dig. J. Nano. Biostr. 6 (2011), 1551-1556.
5. A.R. Ashrafi, M. Mirzargar, PI Szeged and edge
Szeged indices of an infinite family of nanostar
dendrimers, Indian J. Chem. 47A (2008), 538-541.
6. N. Dorosti, A. Iranmanesh. M.V. Diudea,
Computing the Cluj index of dendrimer nanostars,
MATCH Commun. Math. Comput. Chem. 62 (2009),
389-395.
7. J. Braun, A. Kerber, M. Meringer, C. Rucker,
Similarity of molecular descriptors: the equivalence
of Zagreb indices and walk counts, MATCH
Commun. Math. Comput. Chem. 54 (2005), 163-176.
8. K.C. Das, I. Gutman, Some properties of the
second Zagreb index, MATCH Commun. Math.
Comput. Chem. 52 (2004), 103-112.
9. A.A. Dobrynin, R. Entringer, I. Gutman, Wiener
index of trees: Theory and applications, Acta Appl.
Math. 66 (2001), 211-249.
10. A.A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert,
Wiener index of hexagonal systems, Acta Appl.
Math. 72 (2002), 247-294
11. M.R. Farahani, First and second Zagreb
polynomials of VC5C7[p,q] and HC5C7[p,q]
nanotubes, Int. Lett. Chem. Phsy. Astr. 12 (2014), 56-
62.
12. M.R. Farahani, Zagreb indices and Zagreb
polynomials of Polycyclic Aromatic Hydrocarbons
PAHs, J. Chem. Acta 2 (2013), 70-72.
13. G.H. Fath-Tabar, Old and new Zagreb indices of
graphs, MATCH Commun. Math. Comput. Chem. 65
(2011), 79-84.
14. G.H. Fath-Tabar, Zagreb polynomials and PI
indices of some nano-structures, Dig. J. Nanomater.
Bios. 4 (2009), 189-191.
15. I. Gutman, N. Trinajstic, Graph theory and
molecular orbitals, Total electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535-538.
16. I. Gutman, K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83-92.
17. A. Iranmanesh, N.A. Gholami, Computing the Szeged index of styrylbenzene dendrimer and triarylamine dendrimer of generation 1-3, MATCH Commun. Math. Comput. Chem. 62 (2009), 371-379.
18. B. Klajnert, M. Bryszewska, Dendrimers: properties and applications, Acta Biochim. Polonica 48 (2001), 199-208.
19. S. Li, Zagreb polynomials of thorn graphs, Kragujevac J. Sci. 33 (2011), 33-38.
20. M. Mirzagar, PI, Szeged and edge Szeged polynomials of a dendrimer nanostar, MATCH Commun. Math. Comput. Chem. 62 (2009), 363-370.
21. S. Nikolic, G. Kovacevic, A. Milicevic, N. Trinajstic, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), 113-124.
22. H. Wiener, Structural determination of the paraffin boiling points, J. Am. Chem. Soc. 69 (1947), 17-20.
23. H. Yousefi-Azari, A.R. Ashrafi, A. Bahrami, Y. Yazdani, Computing topological indices of some types of benzenoid systems and nanostars, Asian J. Chem. 20 (2008), 15-20.
24. B. Zhou, I. Gutman, Relations between Wiener, hyper-Wiener and Zagreb indices, Chem. Phys. Lett. 394 (2004), 93-95.
25. B. Zhou, Zagreb indices, MATCH Commun. Math. Comput. Chem. 52 (2004), 113-118.
26. B. Zhou, I. Gutman, Further properties of Zagreb indices, MATCH Commun. Math. Comput. Chem. 54 (2005), 233-239.