Journal of Mathematical Chemistry

, Volume 56, Issue 5, pp 1493–1510 | Cite as

Hyper-Wiener and Wiener polarity indices of silicate and oxide frameworks

  • Micheal Arockiaraj
  • S. Ruth Julie Kavitha
  • Krishnan Balasubramanian
  • Ivan Gutman
Original Paper


Molecular descriptors are graph invariants representing the chemical structure in graph-theoretical terms. There is a wide range of such descriptors and the computation of these invariants for the various chemical frameworks is a current area of research. Among these the Wiener types of indices have passed through critical tests and emerged as a useful topological index in QSAR, predictive toxicology and computer-assisted drug discovery as a starting point to reduce a large data set of chemicals. However mathematical techniques to compute hyper-Wiener index continues to pose considerable challenges, as they involve long and complex manipulations. In the present study, we develop a new technique based on vertex cut methods to compute the hyper-Wiener indices of complex silicate and oxide frameworks of current interest for the first time and obtain the analytical expressions of Wiener polarity indices for these chemical frameworks based on vertex neighborhood.


Distance Hyper-Wiener index Silicate network Oxide network 



M. Arockiaraj is supported by Project No. SB/FTP/MS-004/2014, Science and Engineering Research Board, New Delhi, India.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Micheal Arockiaraj
    • 1
  • S. Ruth Julie Kavitha
    • 1
  • Krishnan Balasubramanian
    • 2
  • Ivan Gutman
    • 3
  1. 1.Department of MathematicsLoyola CollegeChennaiIndia
  2. 2.School of Molecular SciencesArizona State UniversityTempeUSA
  3. 3.Faculty of ScienceUniversity of KragujevacKragujevacSerbia

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