Differences between Wiener and modified Wiener indices

Document Type : Original Article


Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 – 136, I R. Iran


The Wiener index is the oldest topological index introduced by H. Wiener for anticipating the boiling point of Paraffin and some other alkenes. An algebraic approach for generalizing the Wiener index is proposed by Graovac and Pisanski for the first time. In this paper, we compute the difference between these topological indices for a class of fullerene graphs.

Graphical Abstract

Differences between Wiener and modified Wiener indices


[1] A. Behmaram, Matching in fullerene and molecular graphs, Ph. D thesis, University of Tehran, 2013.
[2] M. Deza, M. Dutour Sikirić and P. W. Fowler, Zigzags, railroads, and knots in fullerenes, J. Chem. Inf. Comp. Sci. 44 (2004) 1282-1293.
[3] M. Deza and M. Dutour Sikirić, Zigzag structure of complexes, Southeast Asian Bull. Math. 29 (2005) 301.
[4] M. Dutour Sikirić and M. Deza, Space fullerenes: computer search for new Frank-Kasper structures II, Structural Chemistry, 23 (2012) 1103-1114.
[5] M. Dutour Sikirić, O. Delgado-Friedrichs, and M. Deza, Space fullerenes: computer search for new Frank-Kasper structures, Acta Crystallogr. A, 66 (2010) 602-615.
[6] P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Oxford Univ. Press, Oxford, 1995.
[7] M. Ghorbani, Fullerene graphs with pentagons and heptagons, J. Math. Nanosci. 3 (2013) 33-37.
[8] M. Ghorbani and T. Ghorbani, Computing the Wiener index of an infinite class of fullerenes, Studia Ubb Chemia LVIII (2013) 43.
[9] M. Ghorbani and M. Songhori, Computing Wiener index of C12n Fullerenes, Ars. Combin. (accepted).
[10] A. Graovac and T. Pisanski, On the Wiener index of a graph, J. Math. Chem. 8 (1991) 53.
[11] J. E. Graver, Catalog of all fullerenes with ten or more symmetries, Graphs and discovery, 167188, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 69 Amer. Math. Soc., Providence, RI, 2005.
[12] I. Gutman, W. Linert, I. Lukovits and A. A. Dobrynin, Trees with extremal hyper-Wiener index: Mathematical basis and chemical applications, J. Chem. Inf. Comput. Sci. 37 (1997) 349-354.
[13] I. Gutman and L. Šoltés, The range of the Wiener index and its mean isomer degeneracy, Z. Naturforsch., 46a (1991) 865-868.
[14] F. Harary, Graph Theory, Addison-Wesley, Reading, Massachusetts, 1969.
[15] D. J. Klein, I. Lukovits and I. Gutman, On the definition of the hyper-Wiener index for cycle-containing structures, J. Chem. Inf. Comput. Sci. 35 (1995) 50-52.
[16] F. Koorepazan-Moftakhar, A. R. Ashra9i, Distance under Symmetry, Match, 75 (2015) 259-272.
[17] H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl and R. E. Smalley, C60: buckminsterfullerene, Nature 318 (1985) 162-163.
[18] H. J. Wiener, Structural Determination of Paraffin Boiling Points, J. Am. Chem. Soc. 69 (1947) 17-20.
Volume 4, 1-2
June 2014
Pages 19-25
  • Receive Date: 30 September 2013
  • Revise Date: 26 January 2014
  • Accept Date: 23 May 2014
  • First Publish Date: 01 June 2014