An Algebraic Modification of Wiener and Hyper–Wiener Indices and Their Calculations for Fullerenes

  • Fatemeh Koorepazan-Moftakhar
  • Ali Reza AshrafiEmail author
  • Ottorino Ori
  • Mihai V. Putz
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 9)


A molecular graph is a graph in which vertices are atoms and edges are chemical bonds. A graph is called 3-connected, if there does not exist two vertices whose removal disconnects the graph. A fullerene graph is a cubic, planar, and 3-connected whose faces are all pentagons or hexagons. A fullerene is a molecule, that is, its molecular graph is a fullerene graph. In 1991, Graovac and Pisanski (1991) proposed an algebraic modification of the Wiener index of a graph by considering its automorphism group. In this chapter, an algebraic modification for the hyper–Wiener index is presented. These quantities will be computed for some classes of fullerenes.


Wiener index Molecular graph Fullerene 



The first and second authors are partially supported by the University of Kashan under Grant No. 464092/2.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Fatemeh Koorepazan-Moftakhar
    • 1
    • 2
  • Ali Reza Ashrafi
    • 1
    • 2
    Email author
  • Ottorino Ori
    • 3
    • 4
  • Mihai V. Putz
    • 5
    • 6
  1. 1.Department of Nanocomputing, Institute of Nanoscience and NanotechnologyUniversity of KashanKashanIran
  2. 2.Department of Pure Mathematics, Faculty of Mathematical SciencesUniversity of KashanKashanIran
  3. 3.Actinium Chemical ResearchRomeItaly
  4. 4.Laboratory of Computational and Structural Physical-Chemistry for Nanosciences and QSAR, Department of Biology-Chemistry, Faculty of Chemistry, Biology, GeographyWest University of TimişoaraTimişoaraRomania
  5. 5.Laboratory of Computational and Structural Physical-Chemistry for Nanosciences and QSAR, Department of Biology-Chemistry, Faculty of Chemistry, Biology, GeographyWest University of TimişoaraTimişoaraRomania
  6. 6.Laboratory of Renewable Energies-PhotovoltaicsR&D National Institute for Electrochemistry and Condensed MatterTimişoaraRomania

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