Some Bounds on Forgotten Topological Index

K. Agilarasan; A. Selvakumar

doi:https://doi.org/10.14445/22315373/IJMTT-V56P566

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 56 | Number 7 | Year 2018 | Article Id. IJMTT-V56P566 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P566

Some Bounds on Forgotten Topological Index

K. Agilarasan, A. Selvakumar

Citation :

K. Agilarasan, A. Selvakumar, "Some Bounds on Forgotten Topological Index," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 7, pp. 521-523, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P566

Abstract

The forgotten index F(G) is defined as the sum of cubes of the degrees of the vertices of the graph G. In this paper we establish some new upper bounds for the Forgotten Topological index involving the number of vertices, the number of edges and the maximum and minimum vertex degree.

Keywords

Forgotten index.

References

[1] Abdo H, Dimitrov D, Gutman I. On extremal trees with respect to the F−index. Kuwait J Sci. 44(3) (2017) 1-8.
[2] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals, Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538..
[3] I. Gutman, B. Ruščić, N. Trinajstić and C.F. Wilcox, Graph theory and molecular orbitals, XII. Acyclic polyenes, J. Chem. Phys. 62 (1975) 3399–3405.
[4] S. Elumalai, T. Mansour, M.A. Rostami, On the bounds of the forgotten topological index, Turkish J. Math., 41 (2017) 1687 1702.
[5] B. Fortula, I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015) 1184–1190.
[6] T. Balaban, I. Motoc, D. Bonchev and O. Mekenyan, Topological indices for structure activity correlations, Topics Curr. Chem. 114 (1983) 21–55. [7] R. Todeschini and V. Consoni, Handbook of Molecular Descriptors, Wiley-VCH, New York, 2002.
[8] S. Nikolić, G. Kovačević and A. Miličević, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003) 113–124.
[9] I. Gutman, K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004) 83–92.
[10] A. Ilić and B. Zhou, On reformulated Zagreb indices, Discrete App. Math. 160 (2012) 204–209.
[11] K.C. Das, Maximizing the sum of the squares of the degrees of a graph. Discrete Math. 285 (2004), 57–66.
[12] K.C. Das and I. Gutman, Some properties of the second Zagreb index. MATCH Commun. Math. Comput. Chem. 52 (2004), 103–112.
[13] B. Zhou and N. Trinajstić, Some properties of the reformulated Zagreb indices, J. Math. Chem. 48 (2010) 714–719.
[14] A. Ilić, M. Ilić and B. Liu, On the upper bounds for the first zagreb index, Kragujevac Journal of Math. 35 (2011) 173–182.
[15] Sunilkumar M. Hosamani and B. Basavanagoud, New Upper Bounds for the First Zagreb Index, MATCH Commun. Math. Comput. Chem. 74 (2015), 97–101.
[16] J.B. Diaz and F.T. Metcalf, Stronger forms of a class of inequalities of G. Pólya-v and L.V. Kantorovich, Bull. Amer. Math. Soc. 69 (1963), 415–419.
[17] M. Biernacki, H. Pidek, C. Ryll-Naerdzewsk, Sur une inégalité entre des intégrales définies, Univ. Marie Curie-Sklodowska A4 (1950) 1–4.
[18] G.S. Watson, Serial correlation in regression analysis I, Biometrika, 42 (1955), 327–342.
[19] Bo Zhou, N. Trinajstić, On general sum-connectivity index, J. Math. Chem. 47 (2010) 210–218.