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http://dx.doi.org/10.14317/jami.2013.595

ON THE SCHULTZ POLYNOMIAL AND HOSOYA POLYNOMIAL OF CIRCUMCORONENE SERIES OF BENZENOID  

Farahani, Mohammad Reza (Department of Mathematics, Iran University of Science and Technology (IUST))
Publication Information
Journal of applied mathematics & informatics / v.31, no.5_6, 2013 , pp. 595-608 More about this Journal
Abstract
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. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The distance between the vertices $u$ and $v$ in V (G) of graph G is the number of edges in a shortest path connecting them, we denote by $d(u,v)$. In graph theory, we have many invariant polynomials for a graph G. In this paper, we focus on the Schultz polynomial, Modified Schultz polynomial, Hosoya polynomial and their topological indices of a molecular graph circumcoronene series of benzenoid $H_k$ and specially third member from this family. $H_3$ is a basic member from the circumcoronene series of benzenoid and its conclusions are base calculations for the Schultz polynomial and Hosoya polynomial of the circumcoronene series of benzenoid $H_k$ ($k{\geq}3$).
Keywords
Molecular graph; Schultz polynomial; Modified Schultz polynomial; Schultz index; Modified Schultz index; Hosoya polynomial; Wiener index; Circumcoronene; Benzenoid;
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  • Reference
1 S. Klavar A Bird's Eye View of The Cut Method And A Survey of Its Applications In Chemical Graph Theory, MATCH Commun. Math. Comput. Chem 60 (2008), 255-274.
2 S. Klavar and I. Gutman A Comparison of The Schultz Molecular Topological Index with The Wiener Index. J. Chem. Inf. Comput. Sci 36(5) (1996), 1001-1003.   DOI   ScienceOn
3 H.P. Schultz, J. Chem. Inf. Comput. Sci 29 (1989), 227.   DOI   ScienceOn
4 H.P. Schultz, J. Chem. Inf. Comput. Sci 40 (2000), 1158.   DOI   ScienceOn
5 H. Shabani and A.R. Ashrafi Applications of The Matrix Package Matlab in Computing The Hosoya Polynomial of Zig-Zag Nanotubes, Digest. J. Nanomater. Bios 4(3) (2009), 423-428.
6 K. Xu Computing The Hosoya Index And The Wiener Index of An Infinite Class of Dendrimers, Digest. J. Nanomater. Bios 6(1) (2011), 265-270.
7 Sh. Xu and H. Zhang Generalized Hosoya Polynomials of Hexagonal Chains, J. Math. Chem. 43 (2008), 2.
8 M. Eliasi and B. Taeri Schultz Polynomials of Composite Graphs, Appl. Anal. Discrete Math 2 (2008), 285-296.   DOI   ScienceOn
9 M.R. Farahani Schultz polynomial, Modified Schultz polynomial, Hosoya polynomial and Wiener Index of Capra of planar benzenoid: Ca($C_{6}$), Submited (2011).
10 M. Goldberg, J. Tohoku Math 43 (1937), 104-108.
11 I. Gutman, J. Chem. Inform. Comput. Sci 34 (1994), 1087.   DOI   ScienceOn
12 I. Gutman and S. Klazar, M. Petkovsek and P. Zigert On Hosoya Polynomial of benzenoid Graph
13 I. Gutman and S. Klavar A method for calculationg Wiener numbers of benzenoid hy drocarbons and phenylenes, ACH Models Chem 133 (1996), 389-399
14 O. Halakoo, O. Khormali and A. Mahmiani Bounds For Schultz Index of Pentachains, Digest. J. Nanomater. Bios 4(4) (2009), 687-691.
15 A. Heydari On The Modified Schultz Index of $C_4C_8$(S) Nanotubes And Nanororus, Digest. J. Nanomater. Bios 5(1) (2010), 51-56.
16 H. Hosoya, Bull. Chem. Soc. Jpn 44 (1971), 23-32.
17 H. Hosoya On some counting polynomials in chemistry, Discrete Appl. Math 19 (1988), 239-257.   DOI   ScienceOn
18 A. Iranmanesh and Y. Alizadeh Computing Hyper Wiener and Schultz Indices of TUZ$C_6$[p, q] Nanotube By Gap Program, Digest. J. Nanomater. Bios 4(1) (2009), 607-611.
19 A. Iranmanesh and Y. Alizadeh Computing Szeged and Schultz Indices of H $AC_5C_6C_7$[p, q] Nanotube By Gap Program, Digest. J. Nanomater. Bios 4(1) (2009), 67-72.
20 S. Klazar and I. Gutman, Disc. Appl. Math 80 (1997), 73.   DOI   ScienceOn
21 S. Klavar and I. Gutman Bounds for The Schultz Molecular Topological Index of ben zenoid Systems in Terms of Wiener Index, J. Chem. Inf. Comput. Sci 37(4) (1997), 741-744.   DOI   ScienceOn
22 Y. Alizadeh, A. Iranmanesh and S. Mirzaie Computing Schultz Polynomial, Schultz Index of $C_{60}$ Fullerene By Gap Program, Digest. J. Nanomater. Bios 4(1) (2009), 7-10.
23 A.R. Ashrafi and M. Ghorbani A Gap Program For Computing The Hosoya Polynomial and Wiener Index of Nano Structures, Digest. J. Nanomater. Bios 4(2) (2009), 389-393.
24 J. Devillers and A. Balaban, Gordon and Breech Amsterdam. (1999).
25 J.R. Dias From benzenoid hydrocarbons to fullerene carbons, MATCH Commun. Math. Comput. Chem 4 (1996), 57-85.
26 M.V. Diudea, Studia Univ. Babes-Bolyai 4 (2003), 3-21.
27 M.V. Diudea Hosoya polynomial in Tori, MATCH Commun. Math. Comput. Chem 45 (2002), 109-122.
28 A.A. Dobrynin, Croat. Chem. Acta 4 (1999), 869.
29 A. Dress and G. Brinkmann, MATCH Commun. Math. Comput. Chem 33 (1996), 87-100.