ON SECOND HYPER-ZAGREB INDEX OF
CORONA PRODUCTS RELATED TO R-GRAPHS

Abstract

The cognitive and evidential features of the graph discipline are significantly influenced by the implementation of graph operations. Molecular descriptor acts as a fundamental network invariant relevant to a particular molecular structure in the framework of chemical graph theory. The semi-total point graph features the edges of subdivision graph as well as the edges of the original graph. In this paper, we explore combinatorial inequalities associated with the edges, vertices and its corresponding neighborhood notions along with the inclusion of other molecular descriptors in the computations for the determination of exact expressions of second hyper-Zagreb index for certain corona products involving the semi-total point graph.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 3
Year: 2023

DOI: 10.12732/ijam.v36i3.1

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References

  1. [1] C. Berg, G. Forst, Potential Theory on locally Compact Abelian Groups, Springer-Verlag, Berlin-Heidelberg-New York (1975).
  2. [2] S. Cambanis, K. Podgorski, A. Weron, Chaotic behavior of infinitely di- visible processes, Studia Math., 115 (1995), 109-127.
  3. [3] J. Carrasso, W. Kato, On subordinated holomorphic semigroups, Trans. Am. Math. Soc., 327 (1991), 867-878.
  4. [4] I.P. Cornfeld, S.V. Fomin, Y.G. Sinai, Ergodic Theory, Springer-Verlag, Berlin-Heidelberg-New York (1982).
  5. [5] G. Da Prato, J. Zabczyk, Ergodicity for Infinite Dimensional Systems, Cambridge University Press (1996).
  6. [6] F. Hmissi, M. Hmissi, Bochner subordination and ergodicity, Grazer Math. Berichte, 346 (2004), 211-221.
  7. [7] M. Hmissi, H. Mejri, E. Mliki, On ergodicty and mixing for subordinated semigroups, Preprint.
  8. [8] N. Jacob, Pseudo Differential Operators and Markov Process, Vol 1: Fourier Analysis and Semigroups, Imperial College Press, London (2001).
  9. [9] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-Heidelberg-New York (1966).
  10. [10] P. Kokoszka, K. Podgorski, Ergodicity and weak mixing of semistable pro- cesses, Prob. and Math. Stat., 13 (1992), 239-244.
  11. [11] O. Peters, The ergodicity problem in economics, Nat. Phys., 15 (2019), 1216-1221.
  12. [12] O. Peters, A. Adamou, The ergodicity solution of the cooperation puzzle, The Royal Society Collection, 2022.
  13. [13] D. Zhang, H.T. Quan, B. Wu, Ergodicity and Mixing in Quantum Dynam- ics, Phys. Rev. 94, Iss. 2 (2016) 022150.
  14. [14] K. Podgorski, A note on ergodic symmetric stable processes, Stoch. Proc. Appl. 43 (1992), 355-362.
  15. [15] J. Rozinski, T. Zak, The equivalence of ergodicity and weak mixing for infinitely divisible processes, Journal of Theoretical Probability, 10, No 1 (1997), 73-86.
  16. [16] K. Sato, Processes and Infinitely Divisible Distributions, Cambridge Uni- versity Press (1999).
  17. [17] R. Schilling, R. Song, Z. Vondracek, Bernstein Functions. Theory and Ap- plications, De Gruyter Studies in Mathematics 37 (2010).
  18. [18] M.L. Silverstein, Application of the sector condition to the classification of sub- Markovian semigroups, Trans. Amer. Math. Soc., 244 (1978), 103- 146.
  19. [19] A. Vanhoyweghen, B. Verbeken, C. Macharis, et al., The influence of er- godicity on risk affinity of timed and non-timed respondents, Sci. Rep., 12 (2022), 3744.
  20. [20] K. Yoshida, Functional Analysis, Springer-Verlag, Berlin-Heidelberg-New York (1965).