Wiener Polynomials for Multi-Rings Paraffin Structures | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 14, Volume 4, Issue 2, December 2007, Pages 31-40 PDF (282.23 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2007.164025 | ||
| Author | ||
| Ahmed M. Ali | ||
| College of Computer Sciences and Mathematics University of Mosul, Mosul, Iraq | ||
| Abstract | ||
| The distance between any two vertices u and v in a connected graph G is defined as the length of the shortest path between them, and it is denoted by d(u,v).The sum of distances for all unordered pairs of distinct vertices in G represents Wiener index. The number of pairs of vertices G which are distance k apart is denoted by d(G,k), it is clear that the number of d(G,k) is graphical invariant, and the Wiener polynomial of graph G is a generating function of the sequence d(G,k). In this paper, we find the Wiener polynomial of multi-circles of paraffin structural, and this formula which we obtained is better than the formula prove in [5] , because we are able to evaluate coefficients for any limited power of x without depending on the number of circles , and we find the Wiener index and average distance for this structural. Lastly, we contracted a MATLAB program to evaluate the Wiener polynomial coefficient ,Wiener index and average distance. | ||
| Keywords | ||
| Wiener Polynomials; Paraffin Structures | ||
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