Let *G = (V,E) *be a simple connected graph. The sets of vertices and edges of *G* are denoted by *V = V(G)* and* E = E(G)*, respectively. There exist many topological indices and connectivity indices in graph theory. The First and Second Zagreb indices were first introduced by *Gutman* and *Trinajstić* In1972. It is reported that these indices are useful in the study of anti-inflammatory activities of certain chemical instances, and in elsewhere. In this paper, we focus on the structure of ”*G = VC*_{5}C_{7}[p,q]”and ”*H = HC*_{5}C_{7}[p,q]” nanotubes and counting first Zagreb index *Zg*_{1}(G) = ∑_{veV}d_{v2} and Second Zagreb index *Zg*_{2}(G) =∑_{e=uveE(G)}(d_{u}·d_{v}) of *G* and *H*, as well as First Zagreb polynomial *Zg*_{1}(G,x ) =∑_{e=uveE(G)}x^{du+dv} and Second Zagreb Polynomial *Zg*_{2}(G,x) = ∑_{e=uveE(G)}x^{du·dv}

Periodical:

International Letters of Chemistry, Physics and Astronomy (Volume 31)

Pages:

56-62

DOI:

10.18052/www.scipress.com/ILCPA.31.56

Citation:

M. R. Farahani "First and Second Zagreb Polynomials of VC_{5}C_{7}[p,q] and HC_{5}C_{7}[p,q]Nanotubes", International Letters of Chemistry, Physics and Astronomy, Vol. 31, pp. 56-62, 2014

Online since:

Mar 2014

Authors:

Keywords:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

J. Asadpour, R. Mojarad, L. Safikhani, Digest Journal of Nanomaterials and Biostructures 6(3) (2011) 937-941.

A. R. Ashrafi, H. Saadi, M. Ghorbani, Digest Journal of Nanomaterials and Biostructures 3(4) (2008) 227-236.

A. R. Ashrafi, M. Ghorbani, Digest. J. Nanomater. Bios. 4(2) (2009) 389-393.

A. Dobrynin, R. Entringer, I. Gutman, Acta Appl. Math. 66 (2011) 211.

M. R. Farahani. Acta Chim. Slov. 58(4) (2012).

M. R. Farahani, Int. J. Nanoscience & Nanotechnology 8(3) (2012) 175-180.

M. R. Farahani, Advances in Materials and Corrosion 2 (2013) 16-19.

G. H. FathTabar, Digest. J. Nanomater. Bios. 4(1) (2009) 189-191.

I. Gutman, K. C. Das, MATCH Commun. Math. Comput. Chem. 50 (2004) 83-92.

H. Hosoya, Discrete Appl. Math. 19 (1988) 239-257.

A. Iranmanesh, Y. Alizadeh, B. Taherkhani. Int. J. Mol. Sci. 9 (2008) 131-144.

A. Iranmanesh, O. Khormali, J. Comput. Theor. Nanosci. (In press).

Mohammad Reza Farahani, International Letters of Chemistry, Physics and Astronomy 11(1) (2014) 74-80.

D. E. Needham, I. C. Wei, P. G. Seybold. J. Amer. Chem. Soc. 110 (1988) 4186.

G. Rucker, C. Rucker, J. Chem. Inf. Comput. Sci. 39 (1999) 788.

R. Todeschini, V. Consonni. Handbook of Molecular Descriptors. Wiley, Weinheim. (2000).

N. Trinajstić. Chemical Graph Theory. CRC Press, Boca Raton, FL. (1992).

H. Wiener, J. Amer. Chem. Soc. 69(17) (1947) 17-20.

B. Zhou, I. Gutman, Chemical Physics Letters 394 (2004) 93-95. ( Received 20 March 2014; accepted 26 March 2014 ).