On Reciprocals Leap Indices of Graphs

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Ammar Alsinai, Anwar Alwardi, N.D. Soner


In the field of chemical graph theory, topological indices are calculated based on the molecular graph of a chemical compound. Topological indices are used in the development of Quantitative structure Activity/Propoerty Relations. To study the physico-chemical properties of molecules most commonly used are the Zagreb indices. In this paper, we introduce reciprocals leap indices as a modified version of leap Zagreb indices. The exact values of reciprocals leap indices of some well-known classes of graphs are calculated. Lower and upper bounds on the reciprocals leap indices of graphs are established. The relationship between reciprocals leap indices and leap Zagreb indices are presented.

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  1. B. Basavanagoud, P. Jakkannavar, Computing first leap Zagreb index of some nano structures, Int. J. Math. Appl. 6(2-B) (2018), 141-150.
  2. J.A. Bondy, U.S.R. Murty, Graph theory with applications, North Holland, New York, 1976.
  3. S. Fajtlowicz, On conjectures of Grafitti II, Congr. Numer. 60 (1987), 189-197.
  4. I. Gutman, N. Trinajstic, Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535-538.
  5. I. Gutman, Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys. 62 (1975), 3399.
  6. I. Gutman, E. Milovanovi ´c, I. Milovanovic, Beyond the Zagreb indices, AKCE Int. J. Graphs Comb. 17 (2020), 74-85.
  7. F. Harary, Graph Theory, Addison Wesley, Reading Mass, 1969.
  8. A. Milicevic, S. Nikolic, On variable Zagreb indices, Croat. Chem. Acta. 77 (2004), 97-101.
  9. A. M. Naji, N. D. Soner, and I. Gutman, On leap Zagreb indices of graphs, Commun. Comb. Optim. 2 (2017), 99-117.
  10. A. M. Naji, B. Davvaz, S. S. Mahde and N. D. Soner, A study on some properties of leap graphs, Commun. Comb. Optim. 5 (2020), 9-17.
  11. Z. Zhang, J. Zhang, X. Lu, The relation of matching with inverse degree of a graph, Discrete Math. 301 (2005), 243-246.