A graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense related. The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). A directed graph is a graph in which edges have orientation. A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex.  For a simple undirected graph G with order n, and let  denotes its complement. Let δ(G), ∆(G) denotes the minimum degree and maximum degree of G respectively. The complement degree polynomial of G is the polynomial CD[G,x]= , where C

A computational investigation is carried out in the field of charged –particle optics with the aid of numerical analysis method using the personal computer. The work is concerned with the design of electron gun with space-charge effect. The Finite element method (FEM) used in the solution of Poison's equation for determine the axial potential distribution of the two-electrode immersion lens operated under zero magnification condition , and from the solution of the paraxial ray equation the optical properties such as the focal length , spherical and chromatic aberration coefficients are determined, also a calculation of the brightness and perveance for the lens. The electrodes geometry was determined in two and three dimensi

Praise be to God, who created people from one soul, and made her husband, and prayers and peace be upon His Messenger, Mercy given and the grace given, and on a machine and companions pure. Divorce cases have increased in recent years in a worrying manner, especially since divorce has unforeseen consequences at the individual and social levels. The source of concern stems from the fact that the cohesion and integrity of society starts from a family as it is the cornerstone of the social structure, which is the foundation upon which the large society is based. Marital life may suffer from problems and obstacles that are difficult to solve, so the man presents the divorce of his wife and that the phenomenon of divorce is not a result of it, b

The research aims to show the role or extent of the impact of financing in its various forms on the municipal performance before and after the financial deficit through relying on the analytical research methodology of the research community represented by the Directorate General of Municipalities and the Directorate of Maysan municipalities as a sample of research (13) municipal institutions for a period of (8) years, Considering the completion of the final accounts of these years, which provides the necessary data for the study, in addition to the variation in the quality and amounts of grants allocated to municipal institutions during these years, which gives a clearer and more comprehensive picture of the reality of allocatio

The purpose of this paper is to define fuzzy subspaces for fuzzy space of orderings and we prove some results about this definition in which it leads to a lot of new results on fuzzy space of orderings. Also we define the sum and product over such spaces such that: If f = < a1,…,an > and g = < b1,…bm>, their sum and product are f + g = < a1…,an, b1, …, bm> and f × g =. for all a1,…,an,b1,…,bm ? G

The primary purpose of this paper is to introduce the, 2- coprobabilistic normed space, coprobabilistic dual space of 2- coprobabilistic normed space and give some facts that are related of them