Let be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset is a minimum neighborhood dominating set if is a dominating set and if for every holds. The minimum cardinality of the minimum neighborhood dominating set of a graph is called as minimum neighborhood dominating number and it is denoted by . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the smallest number of vertices needed to form a minimum neighborhood-dominating set. The concept of minimum neighborhood dominating set is related to the study of the structure and properties of graphs and is used in various fields such as computer science, operations research, and network design. A minimum neighborhood dominating set is also useful in the study of graph theory and has applications in areas such as network design and control theory. This concept is a variation of the traditional dominating set problem and adds an extra constraint on the intersection of the neighborhoods of the vertices in the set. It is also an NP-hard problem. The main aim of this paper is to study the minimum neighborhood domination number of the split graph of some of the graphs.
Two dwarf snakes were discovered, Eirenis thospitis Schmidtler & Lanza from Sereen mountain, north east of Arbil and E. rothii Jan from Saffin mountain North of Arbil city North of Iraqi Kurdistan. Supported by description and important notes on variation. In addition summarized list for 9 species of the genus Eirenis Jan in Iraq is also presented.
The present study aimed to identify the extent to which the content of social and national studies courses was included in interactive thinking maps in the educational stages in the Kingdom of Saudi Arabia, and to achieve the goal of the study, the researcher used the descriptive and analytical approach, and the study tool used consisted of a content analysis card; Where it included a list of the types of thinking maps, where the study sample consisted of all social and national studies courses at the elementary and intermediate levels, and it is (12) books for the student in its first and second parts, and after verifying the validity and reliability of the tool, it was applied to the study sample, and the study reached conclusions, inc
... Show MoreThis study aimed to manufacture an innovative device that enables the player to walk after the operation and improves the functional efficiency through the improvement in the range of motion as well as the improvement in the size of the muscles working on the knee joint. The research, the study population consisted of players with severing the anterior cruciate ligament of the advanced soccer players, and the number of the research sample was (5) injured for the control sample and (5) for the experimental sample in Abu Ghraib Hospital and some rehabilitation centers for a period of six months, and the pre-tests were conducted after two weeks of The cruciate ligament surgery was performed, and the innovative device was used for the e
... Show MoreThe 1500m race event is part of the athletics system, and the continuous competition to break records and achieve the highest levels of achievement in athletics events, especially the 1500m race event, is one of the topics that occupies the minds of many people interested in achieving digital development for this event, given the distance of the race and the time it takes to complete it. Because it is unique from other events, it has characteristics that distinguish it from other events, despite it being a middle-distance event, which shares with them that its speed is measured by the step, which consists of the length of the step and its frequency. Increasing any of these two factors while keeping one of them constant or increasing
... Show MoreAsthma is a chronic inflammatory disorder of the airways in which many cells and cellular elements play a role. The treatment guidelines recommend theuse of a second controller drug in addition to medium doses of inhaled corticosteroids (ICSs) rather than the use of high doses ICS alone in the treatment of moderate-severe persistent asthma. This study was conducted to compare the clinical efficacy and safety of three treatment regimens in Iraqi patients with moderate-severe persistent asthma.The study included three groups; each group included 15 patients. Patients were administered beclomethasone inhaler alone 1500-2000 μg/day, beclomethasone inhaler 750-1000 μg/day plus oral controlled release aminophylline tablets 450 mg/day or
... Show MoreThis research aims toknow the learning styles according to the model of Felder and Silverman and its relationship to effectively self- perceived mathematicalamong students of the Faculty of Education Pure Sciences - Ibn al-Haytham. By answering the following questions: 1. What are the preferred methods of learning among students in the mathematics department according to the model Felder and Silverman? 2. What is the mathematicalself-perceived levelof the students at the Department of Mathematics effectiveness level? 3. What is the relationship between learning styles according to the Felder model and Silverman and the effectiveness of mathematical self-perceived of the students of the Department of Mathematics? The research sample consiste
... Show MoreThis research aims to analyze the intellectual and civilizational regression that afflicted Iraqi and Arab society due to political and religious tyranny and internal conflicts, which was reflected in the deterioration of human rights values and the absence of equality and justice in dealing with the other religiously, which affected the reluctance of members of religious groups to interact with their national societies and then migrate to Outside, which contributed to a double loss, in terms of the loss of these societies by productive and effective national competencies, and in terms of distorting the image of Islam. The research stressed that the first treatments of this phenomenon are the consolidation of the values of citize
... Show MoreBreastfeeding (BF) serves as a complete nutritional source for the first six months of infant’s life. Breast milk contains all essential nutrients that necessary for the physiological growth and development of infants. The aim of this study was to compare the physiological growth of infants including weight, height and head circumference who were exclusively breastfed for 6 months and those who were given bottle-fed or mixed fed and to find a percentage of exclusive breastfeeding among mothers who contributed in this study in Sulaimani city. This study was carried out in Sulaimani city/ Kurdistan region of Iraq and the cases were enrolled between the first of October 2018 and first of October 2019. The infants’ weight, height and hea
... Show MoreThis paper deals with the subject of demarcating as appropriate scientific techniques to rationalize consumption and to control segments of the society for the technical conduct of its handling of the product depending on the mix of elements (product and the volume of demand, Price, promotion and distribution), but inverse manner designed to adjust the working condition of balance between supply and demand and to ensure that rates continue in the marketing process properly, and therefore the research aims to shed light on some of the practices that reflect the Demarketing techniques, As well as the statement of the reality of attitudes towards the practice of those techniques through a sample survey of officials in Baghdad company for so
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