Vertex Hyper-Zagreb Index of Graphs

  • Authors

    • K. Pattabiraman
    • M. Seenivasan
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.21284
  • Composite graphs, F-index, Hyper-Zagreb index, Topological index, Zagreb index, .
  • In this paper, we obtain the vertex hyper-Zagreb index for some composite graphs. Using the results obtained here, the vertex hyper-Zagreb index for some important classes of graphs are obtained.

     

     

  • References

    1. [1] Ashrafi A.R., Doslic T. and A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math.158,(2010) ,1571-1578.

      [2] Basavanagoud B. and S. Patila, note on hyper-Zagreb index of graph operations, Iran. J.Math. Chem. 7, (2016) , 89 – 92.

      [3] Bollobs B.,and P.Erds, Graphs of extremal weights. Ars Combinato ria, 50, (1998) 225-233.

      [4] Doslic T., Vertex –weighted wiener polynomials for composite graphs, Ars Math. Contemp.1 (2008), 66-80.

      [5] Fath-Tabar G.H, Old and new Zagreb indices of graphs,

      MA TCH Commun.Math.Comput.Chem. 65, (2011), 79-84.

      [6] Furtula B. and I. Gutman, A forgotten topological index, J. Math.

      Chem. 53, (2015), 1184-1190.

      [7] Gao W., Jamil M.K. and M. R. Farahani, The hyper-Zagreb

      index and some graphoperations, J. Appl. Math. Comput. 54(1-2), (2015), 263-275.

      [8] Gutman I., Degree-based topological indices, Croat.Chem. acta 86,

      (2013), 351-361.

      [9] Gutman I., On the origin of two degree –based topological indices,

      Bull.Acad. Serbe Sct.Arts (Cl.Sci.Math.Natur) 146 , (2014 ), 39-52.

      [10] Gutman I., Das K. C, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, (2004), 83-92.

      [11] Gutman I., Furtula B., Kovijanic Vukicevic Z. and G.popivoda,

      Zagreb indices and coindices, MATCH Commun. Math. Comput. Chem. 74, (2015), 5-16.

      [12] Gutman I., Tomovice Z., On the application of line graphs in

      quantitative structure-property studies, J. Serb.Chem. soc. 65, (2000), 577-580.

      [13] Gutman I. and N. Trinajstic, Graph theory and molecular orbitals. Total ψ-electron energy of alternant hydrocarbons. Chemical physics Letters, 17(4), (1972), 535-538.

      [14] Khalifeh M.H, Yousefi-Azari H. and A.R. Ashrafi, The first and second Zagreb indices of some graph operations, Discrete Appl. Math. 157, (2009), 804-811.

      [15] Pattabiraman K. and M. Seenivasan, Bounds on Vertex Zegrab

      Indices of Graphs, Global Journal of Frontier Science Research

      (GJFSR), Volume XVII, IssuseVI,Version1, ( 2017), 43-47.

      [16] Pattabiraman K. and M. Vijayaragavan, Hyper Zagreb indices and its coindices of graphs, Bull. Int. Math. virtual Institute 7,(2017), 31-41.

      [17] Randic M., Characterization of molecular branching. Journal of the

      American Chamical Society ,97(23), (1975), 6609-6615.

      [18] Shirdel G.H., Rezapour H. and A.M. Sayadi, The hyper- Zagreb index of graph operations, Iranian J. Math. Chem.4,(2013),213-220.

      [19] Tavakoli M., Rahbarnia F. and A.R. Ashrafi, Eccentric connectivity and Zagreb coundices of the generalized hierarchical product of graphs, J. Discrete Mathematics . DOI 10.1155/2014/292679 (2014), 5 pages.

      [20] Todeschini R. and V. Consonni, Handbook of molecular descritor (vol.11).John Wiley&sons, (2008).

      Veylaki M., Nikmehr M.J. and H.A. Tavallae, The third and hyper Zagreb coindices of some graph operations, J. Appl.Math. Comput. 50, (2016), 315-325.
  • Downloads

  • How to Cite

    Pattabiraman, K., & Seenivasan, M. (2018). Vertex Hyper-Zagreb Index of Graphs. International Journal of Engineering & Technology, 7(4.10), 573-576. https://doi.org/10.14419/ijet.v7i4.10.21284