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Bounds for the First Zagreb Eccentricity Index and First Zagreb Degree Eccentricity Index

  • Padmapriya, P. (Department of Studies in Mathematics, University of Mysore) ;
  • Veena, Mathad (Department of Studies in Mathematics, University of Mysore)
  • Received : 2017.08.28
  • Accepted : 2018.06.08
  • Published : 2018.06.23

Abstract

The first Zagreb eccentricity index $E_1(G)$ of a graph G is defined as the sum of squares of the eccentricities of the vertices. In this paper some bounds for the first Zagreb eccentricity index and first Zagreb degree eccentricity index are computed.

Keywords

References

  1. M. Biernacki, H. Pidek and C. Ryll-Nardzewsk, Sur une inegalite entre des integrales definies, Ann. Univ. Mariae Curie-Skodowska. Sect. A, 4(1950), 1-4.
  2. P. Biler and A. Witkowski, Problems in Mathematical Analysis, Marcel Dekker, Inc., New York, 1990.
  3. P. S. Bullen, D. S. Mitrinovic and P. M. Vasic, Means and their inequalities, Dordrecht: Reidel, 1988.
  4. N. De, S. M. A. Nayeem and A. Pal, Total eccentricity index of the generalized hier- archical product of graphs, Int. J. Appl. Comput. Math., 1(2015), 503-511. https://doi.org/10.1007/s40819-014-0016-4
  5. J. B. Diaz and F. T. Metcalf, Stronger forms of a class of inequalities of G. Polya-G. Szego and L. V. Kantorovich, Bull. Amer. Math. Soc., 69(1963), 415-418. https://doi.org/10.1090/S0002-9904-1963-10953-2
  6. K. Fathalikhani, H. Faramarzi and H. Yousefi-Azari, Total eccentricity of some graph operations, Electron. Notes Discrete Math., 45(2014), 125-131. https://doi.org/10.1016/j.endm.2013.11.025
  7. M. Ghorbani and M. A. Hosseinzadeh, A new version of Zagreb indices, Filomat, 26(2012), 93-100. https://doi.org/10.2298/FIL1201093G
  8. I. Gutman and N. Trinajstic, Graph theory and molecular orbitals. Total $\pi$- electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17(1972). 535-538. https://doi.org/10.1016/0009-2614(72)85099-1
  9. F. Harary, Graph theory, Addison-Wesley, Reading Mass., 1969.
  10. I. Z. Milovanovc, E. I. Milovanovc and A. Zakic, A short note on graph energy, MATCH Commun. Math. Comput. Chem. 72(2014), 179-182.
  11. D. S. Mitrinovic, Analytic inequalities, Springer-Verlag, Berlin-Heidelberg-New York, 1970.
  12. S. Nikolic, G. Kovacevic, A. Milicevic and N. Trinajstic, The Zagreb indices 30 years after, Croat Chem. Acta, 76(2003), 113-124.
  13. Padmapriya P. and V. Mathad, Zagreb degree eccentricity indices of graphs, Novi Sad J. Math., accepted.
  14. D. Vukicevic and A. Graovac, Note on the comparison of the first and second normalized Zagreb eccentricity indices, Acta Chim. Slov., 57(2010), 524-528.
  15. H. Van de Waterbeemd, R. E. Carter, G. Grassy, H. Kubiny, Y. C. Martin, M. S. Tutte and P. Willet, Glossary of terms used in computational drug design, Pure Appl. Chem., 69(1997), 1137-1152. https://doi.org/10.1351/pac199769051137