On the degree based topological indices of benzene ring embedded in P-type-surface in 2D network

The structure of any finite molecular graph which represent numerical quantities are known as topological indices. The importance of topologicalindices is generally linked with QSAR/QSPR. In this paper, we compute general Zagreb ($M_\alpha$) index, general Randic connectivity ($R_\alpha$) index, general sum-connectivity ($\xi_\alpha$) index, atom-bond connectivity ($ABC$) index and geometric-arithmetic ($GA$) index, $ABC_4$; $GA_5$; multiple Zagreb indices and Zagreb polynomials indices of the benzene ring embedded in P-type-surface in 2D network.

Keywords:

topological indices, multiple Zagreb indices, Zagreb polynomials benzene ring,

PDF

___

K. Yu. Amsharov, M. Jansen, A C78 Fullerene Precursor: Toward the Direct Synthesis of Higher Fullerenes, J. Org. Chem., 73, 2931–2934, 2008.
M. Baca, J. Horvràthovà, M. Mokrišovà, A. Suhànyiovà, On topological indices of fullerenes, Appl. Math. Comput., 251, 154–161, 2015.
A. Q. Baig, M. Imran, H. Ali, S. U. Rehman, Computing topological polynomial of certain nanostructures, J. Optoelectron. Adv. Mat., 17(5-6), 877–883, 2015.
B. Borovicanin, On the extremal Zagreb indices of trees with given number of segments or given number of branching vertices, MATCH Commun. Math. Comput. Chem., 74(1), 57–79, 2015.
S. B. Bozkurt, A. D. Güngör, I. Gutman, and A. S. Çevik, Randic matrix and Randic energy, MATCH Commun. Math. Comput. Chem., 64, 239–250, 2010.
M. Cavers, S. Fallat, and S. Kirkland, On the normalized Laplacian energy and general Randic index R-1 of graphs, Lin. Algebra Appl., 433, 172–190, 2010.
A.A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math., 66, 21–249, 2001.
M. V. Diudea (Ed.), Nanostructures, Novel Architecture, NOVA, New York, 2005.
M. V. Diudea, Cs. L. Nagy, Periodic Nanostructures, Springer, Dordrecht, 2007.
Z. Du, B. Zhou, and N. Trinajstic, On Geometric-Arithmetic Indices of (Molecular) Trees, Unicyclic Graphs and Bicyclic Graphs, MATCH Commun. Math. Comput. Chem., 66, 681– 697, 2011.
M. Eliasi, A. Iranmanesh, I. Gutman, Multiplicative version of first Zagreb index, MATCH Commun. Math. Comput. Chem., 68, 217–230, 2012.
E. Estrada, Atombond connectivity and the energetic of branched alkanes, Chem. Phys. Lett., 463, 422–425, 2008.
E. Estrada, L. Torres, L. Rodriguez, I. Gutman, An atom-bond connectivity index: modelling the enthalpy of formation of alkanes, Indian J. Chem., 37A, 849–855, 1998.
M. Ghorbani, N.Azimi, Note on multiple Zagreb indices, Iran. J. Math. Chem., 3(2), 137– 143, 2012.
M. Ghorbani, M. A. Hosseinzadeh, Computing ABC4 index of nanostar dendrimers, Optoelectron. Adv. Mater. Rapid Commun., 4(9), 1419–1422, 2010.
I. Gutman, B. Furtula, and S. B. Bozkurt, On Randic energy, Lin. Algebra Appl., 442, 50-57, 2014.
I. Gutman, B. Furtula, Z. K. Vukicevic, G. Popivoda, On Zagreb Indices and Coindices, MATCHCommun. Math. Comput. Chem., 74(1), 5–16, 2015.
I. Gutman, B. Rušcic, N. Trinajstic, and C. F. Wilcox, Graph Theory and Molecular Orbitals. XII. Acyclic Polyenes, J. Chem. Phys., 62(9), 3399–3405, 1975.
I. Gutman, J. Tošovic, S. Radenkovic, and S. Markovic, On atom-bond connectivity index. and its chemical applicability, Indian J. Chem., 51A, 690–694, 2012.
A. Gravovac, M. Ghorbani, M. A. Hosseinzadeh, Computing fifth geometric-arithmatic index ABC4 index of nanostar dendrimers, Optoelectron. Adv. Mater. Rapid Commun., 4(9), 1419–1422, 2010.
S. Hayat, M. Imran, On some degree based topological indices of certain nanotubes, J. Comput. Theor. Nanosci., 12(8), 1599–1605, 2015.
S. Hayat, M. Imran, Computation of topological indices of certain networks, Appl. Math. Comput., 240, 213–228, 2014.
S. Hayat, M. Imran, Computation of certain topological indices of nanotubes, J. Comput. Theor. Nanosci., 12(1), 70–76, 2015.
S. Hayat, M. Imran, Computation of certain topological indices of nanotubes covered by C5 and C7, Comput. Theor. Nanosci., 12(4), 533–541, 2015.
X. Li, Y. Shi, A survey on the Randic index, MATCHCommun. Math. Comput. Chem., 59(1), 127–156, 2008.
X. Li, H. Zhao, Trees with the first three smallest and largest generalized topological indices, MATCH Commun. Math. Comput. Chem., 50, 57–62, 2004.
M. ÓKeeffe, G. B. Adams, O. F. Sankey, Predicted new low energy forms of carbon, Phys. Rev. Lett., 68, 2325–2328, 1992.
M. Randic, On characterization of molecular branching., J. Am. Chem. Soc., 97, 6609–6615, 1975.
K. H. Rosen, Discrete Mathematics and its applications, The McGraw-Hill Companies, Inc., seventh edition, 2012.
L. T. Scott, Methods for the chemical synthesis of fullerenes, Angew. Chem. Int. Ed., 43, 4994–5007, 2004.
G. H. Shirdel, H. R. Pour, A. M. Sayadi, The Hyper-Zagreb index of graph operations, Iran. J. Math. Chem., 4(2), 213–220, 2013.
Y. Shi, Note on two generalizations of the Randic index, Appl.Math.Comput., 265, 1019– 1025, 2015.
D. Vukicevic and B. Furtula, J. Math. Chem. 46, 1369–1376, 2009.
B. Zhou, N. Trinajstic, On general sum-connectivity index, J. Math. Chem., 47, 210–218, 2010.