Hyper Zagreb indices of composite graphs

  • Authors

    • Sharmila Devi Kongu Arts and Science College (Autonomous), Erode.
    • V. Kaladevi Bishop Heber College, Trichy
    2016-02-13
    https://doi.org/10.14419/ijams.v6i1.8406
  • Composite graphs, Hyper Zagreb Index.
  • For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the degrees of vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Similarly, the hyper Zagreb index is defined as the sum of square of degree of vertices over all the edges.  In this paper, First we obtain the hyper Zagreb indices of some derived graphs and the generalized transformations graphs. Finally, the hyper Zagreb indices of double, extended double, thorn graph, subdivision vertex corona of graphs, Splice and link graphs are obtained.

  • References

    1. [1] Devilers J., Balaban A.T. (Ed), Topological indices and related descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam, The Netherlands, 1999.

      [2] Gutman I.,Polansky, Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin

      [3] Gutman I., Trinajstic N., Graph theory and molecular orbitals Total p -electron energy of alternant hydrocarbons, Chem. Phy. Lett. 17(1972) 535-538.

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

      [5] Feng L., Ilic A., Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number, Appl. Math. Lett. 23(2010) 943-948.

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

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

      [8] Ashrafi A.R., Doslic T., Hamzeha A., Extremal graphs with respect to the Zagreb coindices, MATCH Commun. Math. Comput. Chem. 65(2011) 85-92.

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

      [10] Hua H., Zhang S., Relations between Zagreb coindices and some distance-based topological indices, MATCH Commun. Math. Comput.Chem. 68(2012) 192-208.

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

      [12] Gutman I., Furtuba B., Kovijanic Uukicevic Z and Popivoda, Zagreb indices and coindices, MATCH commun. Math. Compact. Chem. 74(2013) 5-16.

      [13] Farahani MR., Computing the hyper-zagreb index of hexagonal nanotubes, J. Chem. and Materials Research. 2(2015), 16-18.

      [14] Farahani MP., The hyper-zagreb index of TUSC4C8((S) nanotubes, Int. J. Engg and Tech. Research. 2(2015), 16-18.

      [15] Hua H., Zhang S and Xu K, Further results on the recentic distance sum, Discretre Appl. Math. 160(2012), 170-180

      [16] Alon N, Eigenvalues and expanders, Combinatoria 6(1986), 83-96

      [17] Gutman I., Distance in thorny graph, Publ. Inst. Math. 63(1998) 31-36.

      [18] Kathiresan K.M., Parameswaran C., Certain generalized thorn graphs and their Wiener indices, J. Appl. Math. Inform. 30(2012) 793-807.

      [19] Lu P., Miao Y., Spectra of the subdivision-vertex and subdivision-edge coronae, arXiv:1302.0457v2(2013).

      [20] Walikar H.B., Ramane H.S., Sindagi L., Shirakol S.S., Gutman I., Hosoya polynomial of thorn trees, rods, rings, and stars. Kragujevac J.Sci. 28(2006) 47-56.

      [21] Zhou B., On modified Wiener indices of thorn trees. Kragujevac J. Math. 27(2005) 5-9.

      [22] Doslic., splices, links and their degree weighted wiener polynomials. Graph Theory Notes N.Y. 48(2009), 47-55.

      [23] Sampathkumar E., Chikkodimath S.B., Semitotal graphs of a graph-I, J. Karnatak Univ. Sci. 18(1973) 274-280.

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  • How to Cite

    Devi, S., & Kaladevi, V. (2016). Hyper Zagreb indices of composite graphs. International Journal of Advanced Mathematical Sciences, 4(2), 47-52. https://doi.org/10.14419/ijams.v6i1.8406