Keywords : Wiener polynomial


w-Wiener Polynomials for Width Distance of Some Special Graphs

Ali A. Ali; Asma S. Aziz

AL-Rafidain Journal of Computer Sciences and Mathematics, 2007, Volume 4, Issue 2, Pages 103-124
DOI: 10.33899/csmj.2007.164030

Let G be a k0-connected graph ,and let ,,be the w- width, distance between the two vertices  u,v  in G. The w-Wiener polynomial  of the width distance of G is defined by:
 
 
           
  
Ww(G;x) is obtained in this paper for  some special graphs G such as a cycle , a wheel, a theta graph , a straight hexagonal chain , and Wagner graph .The diameter with respect to the width distance – w, and the Wiener index for each such special graphs are also obtained in this paper.
 

Weiner Polynomials for Generalization of Distance for Some Special Graphs

Ali Aziz Ali; Ahmed M. Ali

AL-Rafidain Journal of Computer Sciences and Mathematics, 2006, Volume 3, Issue 2, Pages 103-120
DOI: 10.33899/csmj.2006.164061

The minimum distance of a vertex v to an set of vertices of a graph G is defined as :
      .
The n-Wiener polynomial for this distance of a graph G is defined as
      ,
where  is the number of order pairs (v,S), , such that
      ,
and  is the diameter for this minimum n-distance.
In this paper, the n-Wiener polynomials for some types of graphs such as complete graphs, bipartite graphs, star graphs, wheel graphs, path and cycle graphs are obtained .The n-Wiener index for each of these special graphs is given. Moreover, some properties of the coefficients of   are established.