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The General Connectivity and General Sum-Connectivity Indices of Nanostructures

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Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G), di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)= The sum-connectivity index is defined as X(G)= The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies.The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)= andmX(G)= where runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).
Rocznik
Tom
Strony
73--80
Opis fizyczny
Bibliogr. 48 poz., rys., wz.
Twórcy
  • Department of Applied Mathematics of Iran University of Science and Technology (IUST), Narmak, Tehran - 16844, Iran
Bibliografia
  • [1] M. Randić, On Characterization of Molecular Branching, J. Am. Chem. Soc., 97(23), 6609 (1975).
  • [2] B. Lucic, N. Trinajstic and B. Zhou, Comparison between the sum-connectivity index and product connectivity index for benzenoid hydrocarbons, Chem. Phys. Lett. 475 (2009), 1-3, 146-148.
  • [3] B. Zhou and N. Trinajstic. On a novel connectivity index. J. Math. Chem. 2009, 46(4), 1252-1270.
  • [4] L. B. Kier and L. H. Hall, Molecular Connectivity in Structure-Activity Analysis, Research Studies Press/Wiley, Letchworth/New York, 1986.
  • [5] L. Pogliani, From molecular connectivity indices to semiempirical connectivity terms: Recent trends in graph theoretical descriptors, Chem. Rev. 100 (2000), 10, 3827-3858.
  • [6] R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley VCH, Weinheim, 2000.
  • [7] I. Gutman and B. Furtula (Editors), Recent Results in the Theory of Randic Index, Math. Chem. Monogr. 6, Univ. Kragujevac, Kragujevac, 2008.
  • [8] X. Li and I. Gutman, Mathematical Aspects of Randic-Type Molecular Structure Descriptors, Math. Chem. Monogr. 1, Univ. Kragujevac, Kragujevac, 2006.
  • [9] B. Bollobas and P. Erdos, Graphs of extremal weights, Ars Combin. 50 (1998), 225-233.
  • [10] J. Devillers and A.T. Balaban (Editors), Topological Indices and Related Descriptors In QSAR and QSPR, Gordon and Breach, Amsterdam, 1999.
  • [11] B. Zhou and N. Trinajstić. On general sum-connectivity index. J. Math. Chem. 2010, 47, 210-218.
  • [12] M. Randić and P. Hansen. J. Chem. Inf. Comput. Sci. 1988, 28, 60.
  • [13] A.R. Ashrafi and P. Nikzad. Connectivity index of the family of dendrimer nanostars. Digest. J. Nanomater. Bios. 2009, 4(2), 269-273.
  • [14] E. Estrada. J. Chem. Inf. Comput. Sci. 1995, 35, 1022.
  • [15] E. Estrada. Chem. Phys. Lett. 1999, 312, 556.
  • [16] Z. Mihali and N. Trinajstić. J. Chem. Educ. 1992, 69(9), 701.
  • [17] D. Morales and O. Araujo. J. Math. Chem. 1993, 13, 95.
  • [18] M.V. Diudea, P. E. John, MATCH Commun. Math. Comput. Chem., 44, 103 (2001).
  • [19] M.V. Diudea, A. Graovac, MATCH Commun. Math. Comput. Chem., 44, 93 (2001).
  • [20] M.V. Diudea, MATCH Commun. Math. Comput. Chem., 45, 109 (2002).
  • [21] S. Yousefi, A. R. Ashrafi, MATCH Commun. Math. Comput. Chem., 56, 169 (2006).
  • [22] X. Li, I. Gutman, Mathematical Chemistry Monographs, 1, 330 (2006).
  • [23] R. Ashrafi, P. Nikzad, Digest Journal of Nanomaterials and Biostructures, 4 (2), 69(2009).
  • [24] M.R. Farahani. Some Connectivity Indices and Zagreb Index of Polyhex Nanotubes. Acta Chim. Slov. 59, 779-783 (2012).
  • [25] M.R. Farahani. Third-Connectivity and Third-sum-Connectivity Indices of Circumcoronene Series of Benzenoid Hk. Acta Chim. Slov. 2013, 60, 198-202.
  • [26] M.R. Farahani. M.P.Vlad. Some Connectivity Indices of Capra-Designed Planar Benzenoid Series Can(C6). Studia Universitatis Babes-Bolyai Chemia. (2014), In press.
  • [27] M.R. Farahani. Second-sum-connectivity index of Capra-designed planar Benzenoid series Can(C6). Polymers Research Journal. 7(3), (2013), Published.
  • [28] M.R. Farahani, K. Kato and M.P.Vlad. Second-sum-connectivity index of Capradesigned planar benzenoid series Can(C6). Studia Universitatis Babes-Bolyai Chemia. 58(2) (2013) 127-132.
  • [29] M.R. Farahani. The second-connectivity and second-sum-connectivity indices of Armchair Polyhex Nanotubes TUAC6[m,n]. Int. Letters of Chemistry, Physics and Astronomy. 11(1), (2014), 74-80.
  • [30] M.R. Farahani. Second-sum-connectivity index of Capra-designed planar Benzenoid series Can(C6). Polymers Research Journal. 7(3), (2013), Published.
  • [31] M.R. Farahani, K. Kato and M.P.Vlad. Second-sum-connectivity index of Capradesigned planar benzenoid series Can(C6). Studia Universitatis Babes-Bolyai Chemia. 58(2) (2013) 127-132.
  • [32] F. Ma and H. Deng. On the sum-connectivity index of cacti. Mathematical and Computer Modelling. February 2011.
  • [33] B. Zhou and N. Trinajstić. On general sum-connectivity index. J. Math. Chem. 2010, 47, 210-218.
  • [34] Z. Du, B. Zhou and N. Trinajstić. Minimum sum-connectivity indices of trees and unicyclic graphs of a given matching number. J. Math. Chem. 2010, 47, 842-855.
  • [35] Z. Du and B. Zhou. On sum-connectivity index of bicyclic graphs. arXiv:0909. 4577v1.
  • [36] Z. Du, B. Zhou and N. Trinajstić. A note on generalized sum-connectivity index. Appl. Math. Lett. 2010, 24, 402-405.
  • [37] R. Xing, B. Zhou and N. Trinajstić. Sum-connectivity index of molecular trees. J. Math. Chem. 2001, 48, 583-591.
  • [38] B. Lucic, S. Nikolic, N. Trinajstic, B. Zhou and S. Ivanis Turk, Sum-connectivity index, in Novel Molecular Structure Descriptors Theory and Applications I, 101-136, Math. Chem. Monogr. 8, Univ. Kragujevac, Kragujevac, (2010)
  • [39] J. Wang, Y. Zhu and G. Liu, On the Randic index of bicyclic graphs, in Recent Results in the Theory of Randic Index, 119-132, Math. Chem. Monogr. 6, Univ. Kragujevac, Kragujevac, (2008).
  • [40] M.V. Diudea, MATCH, Commun. Math. Comput. Chem. 2002, 45, 109-122.
  • [41] A.R. Ashrafi and G.R. Vakili-Nezhaad, Computing the PI index of some chemical graphs related to nanostructures, Journal of Physics: Conference Series, 2006, 29, 181-184.
  • [42] A.S. Yousefi, H. Yousefi-Azari, A.R. Ashrafi and M. H. Khalifeh, Computing Wiener and Szeged Indices of an Achiral Polyhex Nanotorus. JSUT, 2008, 33, 3, 7-11.
  • [43] A. Iranmanesh and Y. Alizadeh, Digest. J. Nanomater. Bios, 2009, 4, 607-611.
  • [44] H. Shabani and A.R. Ashrafi, Digest. J. Nanomater. Bios, 2009, 4, 423-428.
  • [45] S. Alikhani and M.A. Iranmanesh, Chromatic Polynomials of Some Nanotubes. Digest. J. Nanomater. Bios, 2010, 5, 1-7.
  • [46] M.R. Farahani. Fifth Geometric-Arithmetic Index of Polyhex Zigzag TUZC6[m,n] Nanotube and Nanotori. Journal of Advances in Physics. 3(1) (2013) 191-196.
  • [47] M.R. Farahani. Computing GA5 Index of Armchair Polyhex Nanotube, Le Matematiche. (2013), In press.
  • [48] M.R. Farahani, On the Fourth atom-bond connectivity index of Armchair Polyhex Nanotubes. Proc. Rom. Acad., Series B, 15(1) (2013) 3-6.
Typ dokumentu
Bibliografia
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