Keywords : Special graphs
w-Hosoya Polynomials for Connection for Some Special Graphs
AL-Rafidain Journal of Computer Sciences and Mathematics,
2012, Volume 9, Issue 2, Pages 173-184
DOI:
10.33899/csmj.2012.163726
Let and be any two distinct vertices in a connected graph . A container is a set of internally disjoint - paths. The width of is denoted by or is , and the length of is the length of the longest - path in . Then, for a given positive integer w, the width distance between any two distinct vertices u and v in a connected graph is define by: , where the minimum is taken over all containers of width w.
In this paper, we find the Hosoya polynomials, and Wiener indices of the join of two special graphs such as bipartite complete graphs, paths, cycles, star graphs and wheel graphs with respect to the width distance.
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
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.