Keywords : Wiener index


Hosoya Polynomial, Wiener Index, Coloring and Planar of Annihilator Graph of Zn

Mohammed S. Ahmed; Akram Mohammed; Nabeel E. Arif

AL-Rafidain Journal of Computer Sciences and Mathematics, 2020, Volume 14, Issue 2, Pages 41-52
DOI: 10.33899/csmj.2020.167337

Let R be a commutative ring with identity. We consider ΓB(R) an annihilator graph of the commutative ring R. In this paper, we find Hosoya polynomial, Wiener index, Coloring, and Planar annihilator graph of Zn denote ΓB(Zn) , with n= pm or n=pmq, where p, q are distinct prime numbers and m is an integer with m ≥ 1 .
 

Hosoya Polynomials of Generalized Vertex Identified and Edge Introducing Graphs

Ahmed M. Ali; Noor M. Dahash

AL-Rafidain Journal of Computer Sciences and Mathematics, 2013, Volume 10, Issue 3, Pages 77-88
DOI: 10.33899/csmj.2013.163528

The vertex identified and edge introducing graphs of two disjoint connected graphs are extended to n, , disjoint connected graphs. Hosoya polynomials and Wiener indices of such composite graphs are obtained by applying Gutman's Theorem and using mathematical induction on n.
 

w-Wiener Polynomials for Width Distance of the Cartesian Product of K2 with Special Graphs

Ali A. Ali; Asma S. Aziz

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 2, Pages 117-133
DOI: 10.33899/csmj.2008.163989

, be the w- width ,   Let G be a k0-connected graph, and let the distance between the two vertices  u,v  in G. The w-Wiener polynomial of the width distance of G is defined by:
 
 
                                    The w-Wiener polynomials of the Cartesian product of K2with Complete graphKp, Star Sp, Complete bipartite graph Kr,s and path  Pr , are obtained in this paper. The diameter with respect to the width distance-w, and the Wiener index for each such graphs are also obtained.
 

w-Wiener Polynomials of the Width Distance of the Square of a Path and a Cycle and a m-Cubic

Ali A. Ali; Asma S. Aziz

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 1, Pages 11-32
DOI: 10.33899/csmj.2008.163959

Let G be a k0-connected graph ,and let , ,be the w- width distance between the two vertices  u,v  in G. The w-Wiener polynomial of the width distance of G is defined by:
 
 
 
The w-Wiener polynomials of the square of a path , the square of a cycle  ,and of an m-cube  are obtained in this paper . The diameter with respect to the width distance –w ,and the Wiener index for each such graphs are also obtained .
 

Hosoya Polynomials of Steiner Distance of Complete m-partite Graphs and Straight Hexagonal Chains(*)

Ali Aziz Ali; Herish O. Abdullah

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 1, Pages 115-126
DOI: 10.33899/csmj.2008.163953

The Hosoya polynomials of Steiner distance of complete m-partite graphs  and Straight hexagonal chains  are obtained in this paper. The Steiner n-diameter and Wiener index of Steiner n-distance of   and   are also obtained.
 

w-Wiener Polynomials for Width Distance of Some Special Graphs

Ali A. Ali; Asma S. Aziz

AL-Rafidain Journal of Computer Sciences and Mathematics, 2007, Volume 4, Issue 2, Pages 103-124
DOI: 10.33899/csmj.2007.164030

Let G be a k0-connected graph ,and let ,,be the w- width, distance between the two vertices  u,v  in G. The w-Wiener polynomial  of the width distance of G is defined by:
 
 
           
  
Ww(G;x) is obtained in this paper for  some special graphs G such as a cycle , a wheel, a theta graph , a straight hexagonal chain , and Wagner graph .The diameter with respect to the width distance – w, and the Wiener index for each such special graphs are also obtained in this paper.