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AL-Rafidain Journal of Computer Sciences and Mathematics

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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
10.33899/csmj.2006.164061

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Abstract

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.
 
Keywords:
    n-distance Wiener polynomial Special graphs
Main Subjects:
  • Graph Theory
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(2006). Weiner Polynomials for Generalization of Distance for Some Special Graphs. AL-Rafidain Journal of Computer Sciences and Mathematics, 3(2), 103-120. doi: 10.33899/csmj.2006.164061
Ali Aziz Ali; Ahmed M. Ali. "Weiner Polynomials for Generalization of Distance for Some Special Graphs". AL-Rafidain Journal of Computer Sciences and Mathematics, 3, 2, 2006, 103-120. doi: 10.33899/csmj.2006.164061
(2006). 'Weiner Polynomials for Generalization of Distance for Some Special Graphs', AL-Rafidain Journal of Computer Sciences and Mathematics, 3(2), pp. 103-120. doi: 10.33899/csmj.2006.164061
Weiner Polynomials for Generalization of Distance for Some Special Graphs. AL-Rafidain Journal of Computer Sciences and Mathematics, 2006; 3(2): 103-120. doi: 10.33899/csmj.2006.164061
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