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.
In this research has been the manufacture and study the properties of the solar cell type retail hybrid manner thermal evaporation emptiness were studying the properties of the cell at room temperature showed measurements stream circuit behavior linear cell manufacturers reached were calculated efficiency tool cell manufacturers, as well as the expense of workers filling the cell
The study seeks to explore the mental-math level among intermediate-school students. To this end, the researcher raised a question. What the level of mental math among students in the intermediate stage? Total of (576) male and female students were chosen from different schools at Al-karkh side \ general directorate of Baghdad education. So as to answer research question and hypothesis, a questionnaire of (30) items designed by the authors was administered to the study sample. T-test was used to analyze the collected data at the level of significance (0.05). Expectancy means (15) showed significant difference comparing to the achieved mean (10, 10) on mental-math test. The study concluded with students has a low level of mental math. The
... Show MoreThe interim administration is an application of the idea of management required by certain circumstances, which are necessary and urgent, and most laws, especially the laws we have compared (the French Civil Code and the Egyptian civil law and the Iraqi civil law) did not regulate the idea of interim administration accurately, This idea is interrelated, but this idea is highlighted whenever a temporary administrator is needed. It is often necessary to maintain a financial or financial burden that is impossible for the owner to manage his own money for one reason or another, the appointment of a temporary manager who manages these funds, we find the legislator resort in such a case to appoint a manager to temporarily save and ma
... Show MoreThe right to property is one of the most prominent and most important of the fundamental rights that the individual enjoys, whether national or foreign, both of them have their own private property that may not be affected except for the requirements of the country's economic development or what is known as the public benefit, and the Iraqi legislator did not specify what is meant by the removal of foreign investment. Of the bilateral international agreements (BITS), as it determined its terms and methods, the properties of foreign investors may be expropriated in a direct and indirect way.
That interdependence in Islam is cooperation, love and fraternity and give and take
and let him look rich to the poor, every Muslim is himself liable hungry and poor no matter
how many races and colors. That interdependence is cruel, spending for God and is the
greatest supporter of charities that deal with housing, food and medicine for the unemployed
and needy, and social solidarity the consolidation of the values of brotherhood and love,
where is the greatest support of corrupt and concerted community and causes prosperity in
societies and has a significant impact on the unity of Muslims and their club and their
collection. The Islamic regime tops major systems in entrusting the achievement claimed the
lives of
The aim of this investigation is to determine how different weight percentages of alumina nanoparticles, including 0.02, 0.04, and 0.06 percent wt, affect the physical characteristics of Poly Acrylamide (PAAM). Using a hot plate magnetic stirrer, 10 g of poly acrylamide powder was dissolved in 90 g of di-ionized distillate water for 4 hours to produce PAAM with a concentration of 0.11 g/ml. Four sections of the resulting solution, each with a volume of 20 ml, were created. Each solution was added independently with alumina nanoparticles in different ratios 0.0, 0.02, 0.04, and 0.06 to create four nano fluid solutions with different alumina nanoparticle contents based on each weight percent. The hand casting process for n
... Show MoreInterface bonding between asphalt layers has been a topic of international investigation over the last thirty years. In this condition, a number of researchers have made their own techniques and used them to examine the characteristics of pavement interfaces. It is obvious that test findings won't always be comparable to the lack of a globally standard methodology for interface bonding. Also, several kinds of research have shown that factors like temperature, loading conditions, materials, and others have an impact on surface qualities. This study aims to solve this problem by thoroughly investigating interface bond testing that might serve as a basis for a uniform strategy. First, a general explanation of how
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