Consider the (p,q) simple connected graph . The sum absolute values of the spectrum of quotient matrix of a graph  make up the graph's quotient energy. The objective of this study is to examine the quotient energy of identity graphs and zero-divisor graphs  of commutative rings using group theory, graph theory, and applications. In this study, the identity graphs  derived from the group  and a few classes of zero-divisor graphs  of the commutative ring R are examined.

Abstract

Indeed, being busy with the understanding of religion is the best sort of worship that the almighty God has given each period of time a number of scholars and wise men. They receive what has been passed down to them from their great ancestors, and those who are willing to learn will learn, their students preserve their knowledge through teaching and writing. Thus, the scholars were pioneers in this field due to the value and importance of their knowledge. They have strived in learning, explaining, and writing new subjects.

One of those scholars is sheikh (Abdulrahman Al-Penjweni) who passed away 1319 AH in one of the villages of the city of Sulaimani in Iraq. He was one of the wisest scholars, a br

In this paper we introduce the basic of definitions of groups for geometric figures; we describe some of geometric figures by using the properties of groups. The classification of some geometric figures by using the properties of some algebraic structures.

The study of vegetative change of cities is one of the most important studies related to human life because of its direct correlation with the temporal conditions that occur. These include the economic problems that force people to move and look for job opportunities in the city, which leads to an increase in the population density of cities, especially for cities with an important economic and administrative location as in the capital city of Baghdad. In this study, the effect of the increasing in population density was analyzed on the urban planning of Baghdad city. The decreasing in vegetation was due to the increasing of urban areas on the outskirts of the city, which led to an increase in its area. Moreover, urban cities increased t

Background: Crohn's disease (CD) is an immunological disorder associated with chronic inflammatory process of several unspecific regions of gastrointestinal tract but frequently detected in the terminal Ilium and proximal colon or both. This disease frequently presented with various oral manifestations as a consequence of inflammatory process of the disease, nutritional deficiency or medications side effects. Several therapeutic approaches have been developed for CD management that are targeting the inflammatory process and directed at controlling the host immune response. Immunosuppressants such as Azathioprine and anti-TNF α agents as well as the combination of them have been widely used as an effective therapeutic modality with a bett

Background: Fifteen percent of small for gestational age are small as a result of fetal growth restriction, which could be due to maternal, placental or fetal factors. It is an important clinical problem associated with increase perinatal mortality and morbidity. Leptin is a protein that produced by many tissues including the placenta (syncytiotropholoast). Dysregulation of leptin metabolism may be implicated in preeclampsia and IUGR pathogenesis.
Aim of the study: To study the trend of leptin level alteration in maternal serum and cord blood in pregnancies complicated by fetal growth restriction and its relation with fetal outcome.
Methods: An Analytic, cross- sectional study conducted in Al-Elwyia Maternity Teaching Hospital and

Background: Non-nutritive sucking habits are common in infants and toddlers. One of the most common non-nutritive sucking habits is pacifier; its prevalence varies from one population to another. This study was conducted to determine the prevalence of pacifier sucking habit among children aged 1-5 years old in Baghdad city and to assess its effect on the occlusion of primary dentition concerning posterior crossbite. Materials and methods: The study was carried out among 1222 children aged 1-5 years old, from which 50 children with continues pacifier sucking habit were chosen to be the study group, compared to 50 children without any sucking habit (control group) matching the study group in age and gender. Children were examined clinically t

Three stations were chosen on the water treatment plan of al- madaan .The Samples collected from the (Raw water) and the Sedimentation, filtration and storage water and the drinking water of outlet. Coliform densities T.S and F.C and TS and F.S and total bacterial count as bacteriological pollution indicators, as moste probable number (MPN) method was studied in test. Also some of the chemical characteristics of the water like pH , total suspended solid T.S.S, T.D.D.and S04 , T.Hardness , Ca++ , Mg++ . From the results it were indicated . The study showed the drinking water of outlet (distriputed in system) was agree with WHO criteria and Iraqi limits standards .