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

The aerial part of Iraqi Anabasis aphylla (Chenopodiaceae) had been investigated for its alkaloidal contents.The alkaloid anabasine [2-(3-pyridyl)-piperidine] [1] & aphyllidine were isolated from an ethanolic extract of the plant. Isolation of the alkaloid was done by column chromatography followed by preperative thin layer chromatography. Identification of the isolated alkaloid was done by different spectroscopic methods (UV,IR), refractive index & TLC using authentic sample & preparation of a salt.

Alloy of (HgTe) has been prepared succesful in evacuated qurtz ampoule at pressure 4×10-5torr, and melting temperature equal to 823K for five days. Thin films of HgTe of thickness 1μm were deposited on NaCl crystal by thermal evaporation technique at room temperature under vacuum about 4×10-5torr as well as investiagtion in the optical porperties included (absorption coefficient , energy gap) of HgTe films and The optical measurements showed that HgTe film has direct energy gap equal to 0.05 eV. The optical constants (n, k, εr, εi) have been measured over will range (6-28)μm.

A survey of blood parasites among members of two species of Iraqi babblers Timaliidae,
Turodoides caudatus salvadori (de Fillipi, 1865) and Turdoides alterostris (Hartert, 1909)
was carried out in the middle and south of Iraq. Two species of haematozoa were recovered,
Haemoproteus turdoidus sp. nov. and Plasmodium relictum Grassi &Felleti. The description
of the new taxon is provided and discussed with pertinent literature.

The mechanical design of elevator elements is always performed by international standards. The engineer selects the appropriate elements of elevator according to catalogues without knowing scientific details. Therefore, a theoretical analysis is achieved at two operating conditions for guide rails (1) safety gear operation, and (2) running condition with the loads unevenly distributed on the elevator car. The guide rail is considered a continuous beam with variable supports. Then the British code is listed showing the equations used in it.

The theoretical equations showed that guide rails are never subjected to stress in simultaneous combined buckling and bending in the plane, where the bending moment is exerted. It is always a c

Background: Osteoid osteomaa benign tumor is unusual before the age of 5 or after age 30 and is more prevalent in men. The main symptom is pain, which is typically severe and responsible for nocturnal awakenings. The conditons usually diagnosed through radiological imagine and confirmed by Histopathology.
Objectives: To assess the effectiveness and the complications that had been risen during the surgical procedure of osteoid osteoma using en bloc resection.
Methods: (10) Patients diagnosed with osteoid osteomawere treated with enbloc surgical reseaction were included in this study.the study took place at Al Yarmouk teaching hospital.the from April 2017-october 2018 and included 10 patients..(7) male, (3) females.The mean age of th

Vacuum gas oil (611-833)K was distilled from Kirkuk crude oil, which was obtained by blending the following fraction,
light vacuum gas oil (611 - 650) K, medium vacuum gas oil (650-690)K, heavy vacuum gas oil (690-727)K and very
heavy vacuum gas oil (727-833)K.
The vacuum gas oil was hydrotreated on a commercial cobalt-molybdenum alumina catalyst presulfied at specified
condition in a laboratory trickle bed reactor. The reaction temperature varied from (583-643)K over liquid hourly space
velocity ranging between (1.5-3.75)h-1 , Hydrogen pressure was kept constant at 3.5 MPa with a hydrogen to oil ratio
of about 250 L/L
The conversion results for desulfurization appeared to obey the second order kinetics. According to

In the present work, a program for calculating the coefficients of the Aplanatic Cassegrain Telescope (ACT) system, free from the effects of spherical and coma aberrations, were constructed. In addition, the two-mirrors of the optical system, as aspherical surfaces, were adopted. This means, that the two-equations of the mirrors are assumed to be polynomial function of five even terms only. The numerical method, least-squares curve fitting method to calculate the two-mirror coefficients system, was adopted. For choosing the values and ratios that give the best results, Rayleigh Criterion (Rayleigh Limit), for purpose of comparison and preference, was adopted.

This study included the preparation of the dihalogens -1,3 metalla-2[3] ferrocenophanes
like Cp2NbS2Fc,(tBuCp)2NbS2Fc,Cp2NbSe2Fc and (tBuCp)2NbSe2Fe where (Fc=ferrocence)
These complexes has been prepared from the reaction of (R)2 NbCl2 with FCLiM2 ,
where(R=Cp,tBuCp) (M = S,Se) under refluxing in toluene,the reaction was carried under
Argon atmosphere .
These complexes were characterized by elemental microanalysis ,Masse spectra scopy,
nuclear magnetic resonance (
1
HNMR) and melting points .