Hyper Zagreb Indices and its Coindices of Graphs
Abstract
For a (molecular) graph, the hyper Zagreb index is dened asHM(G) = Σuv2E(G) (dG(u) + dG(v))2 and the hyper Zagreb coindex is dened as HM(G) = Σuv=2 E(G) (dG(u)+dG(v))2: In this paper, the hyper Zagreb indices and its coindices of edge corona product graph, double graph and Mycielskian graph are obtained.
References
[1] J. Devillers and A.T. Balaban (Eds.). Topological indices and related descriptors in QSAR and QSPR. Gordon and Breach Science Publishers, Amsterdam, The Netherlands, 1999.
[2] I. Gutman and O.E. Polansky. Mathematical concepts in organic chemistry. Springer-verlag, Berlin 1986.
[3] I. Gutman and N. Trinajstic. Graph theory and molecular orbits. Total Pi-election energy of alternant hydrocarbons. Chem. Phy. Lett., 17(4)(1972), 535-538.
[4] M. H. Khalifeh, H. Yousefi-Azari and A. R. Ashrafi. The first and second Zagreb indices of some graph operations. Discrete Appl. Math., 157(4)(2009), 804-811.
[5] L. Feng and A. Ilic. Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number. Appl. Math. Lett. 23(8)(2010), 943-948.
[6] I. Gutman and K. C. Das. The First Zagerb index 30 years after. MATCH Commun. Math. Comput. Chem., 50(2004), 83-92.
[7] A. R. Ashrafi, T. Doslic and A. Hamzeha. The Zagreb coindices of graph operations. Discrete Appl. Math., 158(16)(2010), 1571-1578.
[8] A. R. Ashrafi, T. Doslic and A. Hamzeha. Extremal graphs with respect to the Zagreb coindices. MATCH Commun. Math.Comput. Chem., 65(1)(2011), 85-92.
[9] T. Doslic. Vertex-weighted Wiener polynomials for composite graphs. Ars Math. Contemp., 1(1)(2008), 66-80.
[10] H. Hua and S. Zhang. Relations between Zagreb coindices and some distance-based topological indices. MATCH Commun. Math.Comput. Chem., 68(1)(2012), 199-208.
[11] G. H. Shirdel. H.Rezapour and A.M. Sayadi. The hyper-Zagreb index of graph operations. Iranian. J. Math. Chem., 4(2)(2013), 213-220.
[12] I. Gutman, B. Furtula, Z. Kovijanic-Vukicevic and G. Popivoda. Zagreb indices and coindices. MATCH Commun. Math. Comput. Chem., 74(1)(2015), 5-16.
[13] M. R. Farahani. Computing the hyper-Zagreb index of hexagonal nanotubes. J. Chem.& Materials Research, 2(1)(2015), 16-18.
[14] M. R. Farahani. The hyper-Zagreb index of TUSC4C8(S) nanotubes. Int. J. Engg.& Tech. Research, 3(1)(2015), 1-6.
[2] I. Gutman and O.E. Polansky. Mathematical concepts in organic chemistry. Springer-verlag, Berlin 1986.
[3] I. Gutman and N. Trinajstic. Graph theory and molecular orbits. Total Pi-election energy of alternant hydrocarbons. Chem. Phy. Lett., 17(4)(1972), 535-538.
[4] M. H. Khalifeh, H. Yousefi-Azari and A. R. Ashrafi. The first and second Zagreb indices of some graph operations. Discrete Appl. Math., 157(4)(2009), 804-811.
[5] L. Feng and A. Ilic. Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number. Appl. Math. Lett. 23(8)(2010), 943-948.
[6] I. Gutman and K. C. Das. The First Zagerb index 30 years after. MATCH Commun. Math. Comput. Chem., 50(2004), 83-92.
[7] A. R. Ashrafi, T. Doslic and A. Hamzeha. The Zagreb coindices of graph operations. Discrete Appl. Math., 158(16)(2010), 1571-1578.
[8] A. R. Ashrafi, T. Doslic and A. Hamzeha. Extremal graphs with respect to the Zagreb coindices. MATCH Commun. Math.Comput. Chem., 65(1)(2011), 85-92.
[9] T. Doslic. Vertex-weighted Wiener polynomials for composite graphs. Ars Math. Contemp., 1(1)(2008), 66-80.
[10] H. Hua and S. Zhang. Relations between Zagreb coindices and some distance-based topological indices. MATCH Commun. Math.Comput. Chem., 68(1)(2012), 199-208.
[11] G. H. Shirdel. H.Rezapour and A.M. Sayadi. The hyper-Zagreb index of graph operations. Iranian. J. Math. Chem., 4(2)(2013), 213-220.
[12] I. Gutman, B. Furtula, Z. Kovijanic-Vukicevic and G. Popivoda. Zagreb indices and coindices. MATCH Commun. Math. Comput. Chem., 74(1)(2015), 5-16.
[13] M. R. Farahani. Computing the hyper-Zagreb index of hexagonal nanotubes. J. Chem.& Materials Research, 2(1)(2015), 16-18.
[14] M. R. Farahani. The hyper-Zagreb index of TUSC4C8(S) nanotubes. Int. J. Engg.& Tech. Research, 3(1)(2015), 1-6.
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2016-12-30
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