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On the multiplicative Zagreb coindex of graphs

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Języki publikacji
EN
Abstrakty
EN
For a (molecular) graph G with vertex set V (G) and edge set E(G), the first and second Zagreb indices of G are defined as [formula] and [formula] respectively, where dG(v) is the degree of vertex v in G. The alternative expression of M1 (G) is [formula]. Recently Ashrafi, Doslic and Hamzeh introduced two related graphical invariants [formula] and [formula] named as first Zagreb coindex and second Zagreb coindex, respectively. Here we define two new graphical invariants [formula] and [formula] as the respective multiplicative versions of [formula]. In this paper, we have reported some properties, especially upper and lower bounds, for these two graph invariants of connected (molecular) graphs. Moreover, some corresponding extremal graphs have been characterized with respect to these two indices.
Słowa kluczowe
Rocznik
Strony
191--204
Opis fizyczny
Bibliogr. 28 poz., rys.
Twórcy
autor
autor
autor
  • Nanjing University of Aeronautics and Astronautics, College of Science, Nanjing, Jiangsu 210016, PR China, kexxu1221@126.com
Bibliografia
  • [1] A.R. Ashrafi, T. Doslic, A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010), 1571-1578.
  • [2] A.R. Ashrafi, T. Doslic, A. Hamzeh, Extremal graphs with respect to the Zagreb coindices, MATCH Commun. Math. Comput. Chem. 65 (2011), 85-92.
  • [3] A.T. Balaban, I. Motoc, D. Bonchev, O. Mekenyan, Topological indices for structure-activity corrections, Topics Curr. Chem. 114 (1983), 21-55.
  • [4] J.A. Bondy, U.S.R. Murty, Graph Theory with Applications, Macmillan Press, New York, 1976.
  • [5] K.C. Das, I. Gutman, B. Zhou, New upper bounds on Zagreb indices, J. Math. Chem. 46 (2009), 514-521.
  • [6] K.C. Das, I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem. 52 (2004), 103-112.
  • [7] H. Deng, A unified approach to the extremal Zagreb indices for trees, unicyclic graphs and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 57 (2007), 597-616.
  • [8] T. Doslic, Vertex-weighted Wiener polynomials for composite graphs, Ars Math. Con-temp. 1 (2008), 66-80.
  • [9] M. Eliasi, A. Iranmanesh, I. Gutman, Multiplicative versions of first Zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), 217-230.
  • [10] I. Gutman, Multiplicative Zagreb indices of trees, Bulletin of Society of Mathematicians Banja Luka 18 (2011), 17-23.
  • [11] I. Gutman, K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83-92.
  • [12] I. Gutman, M. Ghorbani, Some properties of the Narumi-Katayama index, Appl. Math. Lett. 25 (2012), 1435-1438.
  • [13] I. Gutman, O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, 1986.
  • [14] I. Gutman, N. Trinajstic, Graph theory and molecular orbitals. III. Total -K-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535-538.
  • [15] I. Gutman, B. Ruscic, N. Trinajstic, C.F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys. 62 (1975), 3399-3405.
  • [16] A.J. Hoffman, R.R. Singleton, On Moore graphs with diameters 2 and 3, IBM J. Res. Develop. 4 (1960), 497-504.
  • [17] A. Ilic, D. Stevanovic, On comparing Zagreb indices, MATCH Commun. Math. Comput. Chem. 62 (2009), 681-687.
  • [18] B. Liu, Z. You, A survey on comparing Zagreb indices, MATCH Commun. Math. Comput. Chem. 65 (2011), 581-593.
  • [19] S. Nikolic, G. Kovacevic, A. Milicevic, N. Trinajstic, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003) 113-124.
  • [20] R. Todeschini, D. Ballabio, V. Consonni, Novel molecular descriptors based on functions of new vertex degrees [in:] Novel molecular structure descriptors - Theory and applications I, I. Gutman, B. Furtula, (eds.), pp. 73-100. Univ. Kragujevac, Kragujevac, 2010.
  • [21] R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Wein-heim, 2000.
  • [22] R. Todeschini, V. Consonni, New local vertex invariants and molecular descriptors based on functions of the vertex degrees, MATCH Commun. Math. Comput. Chem. 64 (2010), 359-372.
  • [23] N. Trinajstic, Chemical Graph Theory, CRC Press, Boca Raton, FL, 1992.
  • [24] K. Xu, The Zagreb indices of graphs with a given clique number, Appl. Math. Lett. 24 (2011), 1026-1030.
  • [25] K. Xu, I. Gutman, The largest Hosoya index of bicyclic graphs with given maximum degree, MATCH Commun. Math. Comput. Chem. 66 (2011), 795-824.
  • [26] K. Xu, K.C. Das, Trees, unicyclic, and bicyclic graphs extremal with respect to multiplicative sum Zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), 257-272.
  • [27] K. Xu, H. Hua, A unified approach to extremal multiplicative Zagreb indices for trees, unicyclic and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 68 (2012), 241-256.
  • [28] S. Yamaguchi, Estimating the Zagreb indices and the spectral radius of triangle- and quadrangle-free connected graphs, Chem. Phys. Lett. 458 (2008), 396-398.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0009-0017
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