On the Graovac-Pisanski index

The Graovac-Pisanski index ( GP index) is an algebraic approach for generalizing the Wiener index. In this paper, we co mpute the difference between the Wiener and GP indices for an infinite family of polyhedral graph s.

[1]  H. Wiener.  Structural determination of paraffin boiling points. , 1947, Journal of the American Chemical Society.

[2]  Ali Reza Ashrafi,et al.  The modified Wiener index of some graph operations , 2016, Ars Math. Contemp..

[3]  Hong Lin.  A Note on the Maximal Wiener Index of Trees with Given Number of Vertices of Maximum Degree , 2014 .

[4]  Yong Liu,et al.  Maximum Wiener Index of Trees with Given Degree Sequence , 2010 .

[5]  A. Ashrafi,et al.  PI and Omega Polynomials of IPR Fullerenes , 2010 .

[6]  Hong Lin.  A Congruence Relation for the Wiener Index of Trees with Path Factors , 2013 .

[7]  Ali Reza Ashrafi,et al.  Distance Under Symmetry: (3,6)-Fullerenes , 2016 .

[8]  A. Ashrafi,et al.  The PI and Edge Szeged Polynomials of an Infinite Family of Fullerenes , 2010 .

[9]  COMPUTING VERTEX PI, OMEGA AND SADHANA POLYNOMIALS OF F12 (2N+1) FULLERENES , 2010 .

[10]  Modjtaba Ghorbani,et al.  Study of fullerenes via their symmetry groups , 2017 .

[11]  Stephan Wagner.  A Class of Trees and its Wiener Index , 2006 .

[12]  Li-Qun Xu,et al.  The Wiener Index of Trees with Given Degree Sequences , 2008 .

[13]  Ali Reza Ashrafi,et al.  Distance, Symmetry, and Topology in Carbon Nanomaterials , 2016 .

[14]  I. Gutman,et al.  ON THE TERMINAL WIENER INDEX OF THORN GRAPHS , 2010 .

[15]  Sandi Klavzar,et al.  A theorem on Wiener-type invariants for isometric subgraphs of hypercubes , 2006, Appl. Math. Lett..

[16]  Hong Lin.  Extremal Wiener Index of Trees with Given Number of Vertices of Even Degree , 2014 .

[17]  I. Gutman,et al.  Wiener Index of Hexagonal Systems , 2002 .

[18]  Hongying Lin,et al.  Extremal Wiener Index of Trees with All Degrees Odd , 2013 .

[19]  Modjtaba Ghorbani,et al.  An algebraic study of non classical fullerenes , 2016 .

[20]  Harishchandra S. Ramane,et al.  ON THE WIENER INDEX OF A GRAPH , 2012 .

[21]  Ivan Gutman,et al.  The Range of the Wiener Index and Its Mean Isomer Degeneracy , 1991 .

[22]  Bo Zhou,et al.  The Kirchhoff index and the matching number , 2009 .

[23]  István Lukovits,et al.  On the Definition of the Hyper-Wiener Index for Cycle-Containing Structures , 1995, J. Chem. Inf. Comput. Sci..

[24]  Sandi Klavzar,et al.  Modified Wiener index via canonical metric representation, and some fullerene patches , 2016, Ars Math. Contemp..

[26]  I. Gutman,et al.  Wiener Index of Trees: Theory and Applications , 2001 .

[27]  M. Ghorbani,et al.  Differences between Wiener and modified Wiener indices , 2014 .

[28]  Ivan Gutman,et al.  Vertex Version of the Wiener Theorem , 2014 .

[29]  Ante Graovac,et al.  Variable Wiener Indices of Thorn Graphs , 2006 .

[30]  Ante Graovac,et al.  On Modified Wiener Indices of Thorn Graphs , 2004 .

[31]  Sandi Klavzar,et al.  Algebraic Approach to Fasciagraphs and Rotagraphs , 1996, Discret. Appl. Math..

[32]  Stephan Wagner.  A Note on the Inverse Problem for the Wiener Index , 2010 .

[33]  Modjtaba Ghorbani,et al.  An algebraic approach to Wiener number , 2017 .

[34]  Ali Reza Ashrafi,et al.  Topological Symmetry of Nanostructures , 2015 .