Keywords : n-distance


The n-Hosoya Polynomial of 𝑊𝛼⊠ Cβ

Ahmed M. Ali; Haveen G. Ahmed

AL-Rafidain Journal of Computer Sciences and Mathematics, 2012, Volume 9, Issue 2, Pages 139-150
DOI: 10.33899/csmj.2012.163707

For a wheel  and a cycle  the composite graphs ⊠  is constructed from the union of  and  and  adding the edges  and  , where  is an edge of  and is an edge of . The n – diameter , the  n – Hosoya polynomial and the n – Wiener index of  ⊠  are obtained in this paper.
 

The n-Wiener Polynomials of the Cartesian Product of a Complete Graph with some Special Graphs

Ali Aziz Ali; Haveen G. Ahmed

AL-Rafidain Journal of Computer Sciences and Mathematics, 2009, Volume 6, Issue 2, Pages 117-128
DOI: 10.33899/csmj.2009.163802

The n-Wiener polynomials of the Cartesian products of a complete graph Kt with another complete graph Kr, a star graph Sr, a complete bipartite graph Kr,s, a wheel Wr, and a path graph Pr are obtained in this paper. The n-diameters and the n-Wiener indices of Kt×Kr, Kt×Sr, Kt×Kr,s, Kt×Wr and Kt×Pr are also obtained.
 

Weiner Polynomials to Generalize the Distance of Some Composite Graphs from Special Graphs

Ali Aziz Ali; Ahmed M. Ali

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 2, Pages 29-45
DOI: 10.33899/csmj.2008.163984

It is not easy to find the Wiener polynomials for generalized distance of  compound graphs constructed in the form and  for any two disjoint connected graphs and .Therefore, in this paper, we obtain Wiener polynomials for generalized distance of and  when and  are special graphs such as complete graphs, and stars. The Wiener index of each such graph with respect to the generalized distance is also obtained in this paper.
            The Wiener polynomial for the generalized distance of the join of any two disjoint connected graphs is 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.