Weiner Polynomials for Generalization of Distance for Some Special Graphs
AL-Rafidain Journal of Computer Sciences and Mathematics,
2006, Volume 3, Issue 2, Pages 103-120
AbstractThe 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.
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