Note on edge distance-balanced graphs

Document Type : Research Paper



Edge distance-balanced graphs are graphs in which for every edge $e = uv$ the number of edges closer to vertex $u$ than to vertex $v$ is equal to the number of edges closer to $v$ than to $u$. In this paper, we study this property under some graph operations.


Main Subjects

M. Aouchiche and P. Hansen (2010). on a conjecture about the Szeged index. European J . Combin.. 31, 1662-1666 A. T. Balaban, P. V. Khadikar and S. Aziz (2010). Comparison of topological indices based on iterated `sum' versus `product' operations. Iran. J. Math. Chem.. 1, 43-60 T. Doslic (2008). Vertex-Weighted Wiener polynomials for composite graphs,. Ars Math. Contemp.. 1, 66-80 K. Handa (1999). Bipartite graphs with balanced (a,b)-partitions. Ars Combin.. 51, 113-119 A. Ilic, S. Klavzar and M. Milanovic (2010). on distance-balanced graphs. European J. Combin.. 31, 733-737 W. Imrich, S. Klavzar (2000). Product Graphs: Structure and Recognition. Wiley, New York, USA. J. Jerebic, S. Klavzar, D. F. Rall (2008). Distance-balanced graphs. Ann. Combin.. 12, 71-79 M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi (2008). The hyper-Wiener index of graph operations. Comput. Math. Appl.. 56, 1402-1407 M. K. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi and S. G. Wagner (2009). Some new results on distance-based graph invariants. European J. Combin.. 30, 1149-1163 D. Stevanovic (2001). Hosoya polynomial of composite graphs. Discrete Math.. 235, 237-244 M. Tavakoli and H. Yousefi-Azari (2010). Computing PI and hyper-Wiener indices of corona product of some graphs. Iran. J. Math. Chem.. 1, 131-135 W. Yan, B.-Y Yang, Y.-N Yeh (2007). The behavior of Wiener indices and polynomials of graphs under five graph decorations. Appl. Math. Lett.. 20, 290-295 Y. N. Yeh and I. Gutman (1994). On the sum of all distances in composite graphs. Discrete Math.. 135, 359-365
  • Receive Date: 03 August 2011
  • Revise Date: 17 September 2011
  • Accept Date: 17 September 2011
  • Published Online: 01 March 2012