Topological indices provide important insights into the structural characteristics of molecular graphs. The present investigation proposes and explores a creative graph on a finite group G, which is known as the RIG. This graph is designated as ΓRS G2(4) indicating a simple undirected graph containing elements of G. Two distinct ertices are regarded as nearly the same if and only if their sum yields a non-trivial involution element in G. RIGs have been discovered in various finite groups. We examine several facets of the RIG by altering the graph through the conjugacy classes of G. Furthermore, we investigate the topological indices as applications in graph theory applying the distance matrix of the G2(4) group.

Agricultural development occupies an important position in the economies of developing countries, and its role is greater for the Arab countries. The first task is to provide food security for all the population through sustainable development, which includes the investment of available natural resources and employment opportunities for the rural population, As well as the provision of raw materials for agricultural processing in order to increase agricultural exports to reduce the balance of payments deficit. Sustainable development is linked to increased production and improvement, as well as to food security. On the one hand, it has to cope with the increase in population and if it is possible to achieve a surplus allocated for export, a

Tobacco products of all kinds are harmful to public health, so legislation has paid great attention to regulating the process of tobacco production and distribution, whether at the level of national or international legislation, in a way that achieves legal protection for these products, so the establishment of civil liability for tobacco companies as a result of harm to the smoker The positive and the negative provoked a jurisprudential dispute due to the specificity of the work of these companies, and the jurisprudence differed in the legal nature of tobacco companies ’liability between contractual and tort liability in a way that enables the injured smoker to obtain his right to compensation.

The present study aims at analyzing the polysemy of the English preposition in from the cognitive linguistic (CL) point of view using Evans' and Tyler's approach (2003). The perplexity faced by Iraqi second language learners (L2) due to the multi-usages of this preposition has motivated the researcher to conduct this study. Seventy-six second year university students participated in this experimental study. The data of the pre-test and post-test were analyzed by SPSS statistical editor. The results have shown the following: First, a progress of more than (0.05≤) has been detected as far as students' understanding of the multiple usages of the preposition in is concerned. Second, the results of the questionnaire have s

The survey and checklist of invasive species of the insects in some different localities of Iraq are revised; 24 invasive species were documented until December 2018 during the current investigations. The species distributions, common names and synonyms are given.

The current investigation included all of exotic species in Iraq, which are not collected during this study.

Background: Mondor's disease means superficial thrombophlibitis of the chest wall in human, treatment is entirely symptomatic. Hot, wet dressing and anodynes may be used for pain relief.
Objective: To evaluate the role of systemic and transdermal action of diclofenac (olfen) with respect to the symptom and sign (pain, erythema along the superficial vein), and the use of Doppler ultrasonography which is a colored ultrasound used for assessment of flow of blood in vessels.
Method: The study was performed on 12 cases with Mondor's disease in middle age female patients with the involvement of lnframammary veins in all of the them (commonly affected), 4 cases had reassurance only, 4 cases had reassurance with systemic diclofenac, and th

The research current (Comment formal for Hruvijat in contemporary Iraqi porcelain). In an attempt to study the Arab character that inspired the Iraqi artist of all intellectual its terms of reference and stylistic by taking advantage of the cultural heritage and the rebuilding of the character to create a system ride of relationships that focus on structural body ceramic body ideas and multiple implications are invested in the structural fabric of the products of contemporary ceramic .vdila for ways to achieve and processing techniques and transmission of functional specificity (blogging) and cosmetic particularly to semantics derive from the content and expresses itself templates ceramic raw materials and by building works of art in pla

Background: Determination of sex and estimation of stature from the skeleton is vital to medicolegal investigations. Skull is composed of hard tissue and is the best preserved part of skeleton after death, hence, in many cases it is the only available part for forensic examination. Lateral cephalogram is ideal for the skull examination as it gives details of various anatomical points in a single radiograph. This study was undertaken to evaluate the accuracy of digital cephalometric system as quick, easy and reproducible supplement tool in sex determination in Iraqi samples in different age range using certain linear and angular craniofacial measurements in predicting sex. Materials and Method The sample consisted of 113of true lateral cepha

This research aims to solve the nonlinear model formulated in a system of differential equations with an initial value problem (IVP) represented in COVID-19 mathematical epidemiology model as an application using new approach: Approximate Shrunken are proposed to solve such model under investigation, which combines classic numerical method and numerical simulation techniques in an effective statistical form which is shrunken estimation formula. Two numerical simulation methods are used firstly to solve this model: Mean Monte Carlo Runge-Kutta and Mean Latin Hypercube Runge-Kutta Methods. Then two approximate simulation methods are proposed to solve the current study. The results of the proposed approximate shrunken methods and the numerical

The research aims to identify the role of community participation in achieving organizational distinction in the Dhulia's municipality, which is one of the formations of the Ministry of Construction, Housing, Municipalities and Public Works in Salah al-Din Governorate, which is one of the service organizations that have a fundamental role in providing service to the community, which has faced many administrative challenges and many problems caused by the rapid and continuous changes in the environment, therefore modern management concepts must be adopted, such as community participation and the knowledge of its role To achieve its goals, which helps it in facing changes as well as achieving organizational excelle