Main Subjects : Graph Theory


Schultz and Modified Schultz Polynomials for Vertex – Identification Chain and Ring – for Hexagon Graphs

Mahmood M. Abdullah; Ahmed M. Ali

AL-Rafidain Journal of Computer Sciences and Mathematics, 2021, Volume 15, Issue 1, Pages 25-38
DOI: 10.33899/csmj.2021.168251

The aim of this paper is to find polynomials related to Schultz, and modified Schultz indices of vertex identification chain and ring for hexagonal rings (6 – cycles). Also to find index and average index of all of them.

The n-Hosoya Polynomials of the Square of a Path and of a Cycle

Ahmed M. Ali

AL-Rafidain Journal of Computer Sciences and Mathematics, 2021, Volume 15, Issue 1, Pages 13-24
DOI: 10.33899/csmj.2021.168250

The n-Hosoya polynomial of a connected graph G of order t is defined by:
Hn (G;x) = ∑ Cn (G;x) xk, where, Cn(G,k) is the number of pairs (v,S), in which |S| = n -1, 3 ≤ n ≤ t, v  V(G) ,  S  V (G) , such that dn(v,S) = k , for each 0 ≤ k ≤ δn. In this paper, we find the n-Hosoya polynomial of the square of a path and of the square of a cycle. Also, the n-diameter and n-Wiener index of each of the two graphsare determined
 

The Basis Number of Symmetric Difference of K2 with Some Ladder Graphs

Ahmed M. Ali; Rasha S. Hasan

AL-Rafidain Journal of Computer Sciences and Mathematics, 2021, Volume 15, Issue 1, Pages 13-22
DOI: 10.33899/csmj.2021.168256

The basis number of a graph  G  is  defined to be the least integer  k  such that  G  has  a  k-fold cycle  basis.  We investigate the basis number of symmetric difference of K2 with a ladder graph Lm , acircular ladder, and a Möbius ladder.

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 .
 

The Restricted Detour Polynomial of the Theta Graph

Herish O. Abdullah; Ivan D. Ali

AL-Rafidain Journal of Computer Sciences and Mathematics, 2020, Volume 14, Issue 1, Pages 13-20
DOI: 10.33899/csmj.2020.164664

The restricted detour distance  D*(u,v) between two vertices u and v of a connected graph G is the length of a longest u - v path P in G such that <V(P)> = P. The main goal of this paper is to obtain the restricted detour polynomial of the theta graph. Moreover, the restricted detour index of the theta graph will also be obtained.
 

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
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.