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.
The research aims to estimate missing values using covariance analysis method Coons way to the variable response or dependent variable that represents the main character studied in a type of multi-factor designs experiments called split block-design (SBED) so as to increase the accuracy of the analysis results and the accuracy of statistical tests based on this type of designs. as it was noted in the theoretical aspect to the design of dissident sectors and statistical analysis have to analyze the variation in the experience of experiment )SBED) and the use of covariance way coons analysis according to two methods to estimate the missing value, either in the practical side of it has been implemented field experiment wheat crop in
... Show MoreThe research tagged (the image of the soldier in contemporary Iraqi painting) dealt with the concept of the image as one of the basic concepts in the creative achievement, whether it is in the field of art, literature or beauty. Therefore, the concept of the image expanded to express the various aspects of human creativity, including the field of painting. To know the image of the soldier in contemporary Iraqi painting, the research included four chapters. The first chapter focused on the methodological framework of the research, while the second chapter included three sections. The first topic dealt with the philosophical and artistic concept of the image. The second topic was concerned with the representations of the soldier's image in
... Show Moreالعراق وسياسة حسن الجوار تجاه تركيا
Air pollution is considered one of the major environmental problems that contain many challenges and difficulties facing most countries of the world, including Iraq. The problem has emerged widely with the emergence of the industrial revolution in the world and the tremendous increase in the population and the increase in the number of transportation and its development in addition to excavation, maintenance and work Construction and weather fluctuations, such as dust and sandstorms, pollution resulting from oil refining, extraction, diversion and other processes that cause pollution, and the start of the world using methods that limit the volume of environmental pollution. The most prominent of these methods is the imposition of
... Show MoreThis research attempts to evaluate the role of the information system by highlighting its importance in providing date and information to the tax administration the process of tax accounting for those who are subject to income tax whether they are individuals or companies where the effective information system provides accurate and reliable information in a timely manner.
At the theoretical part of the research, the research approaches the problem of the research represented in that whether the information system, applied in the General Commission for Taxes, is capable of achieving its role in reducing the phenomenon of tax evasion. The existence of a set of things which in the Commission may lead to increase tax evasion by taxpa
... Show Moreملخص البحث: تعتبر مشكلة تعاطي المخدرات من المشكلات التي تؤثر في بناء المجتمع وأفراده لما يترتب عليها من آثار اجتماعية واقتصادية ونفسية سيئة تنسحب على الفرد و على المجتمع، كما أنها ظاهرة اجتماعية مرضية تدفع إليها عوامل عديدة؛ بعضها يتعلق بالفرد والبعض الآخر بالأسرة والثالث بالبناء الاجتماعي ككل. وتعد ظاهرة انتشار المخدرات من الظواهر الأكثر تعقيدا وبارزة هذه الظاهر ة وإحدى مشكلات العصر، الشاملة في المجتمع، و
... Show MoreThis dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermor
... Show MoreThis thesis aims to show the effects of the development of the traditional manual system of the tax accounting process to the electronic system by the activation of the tax identification numbers (TINs) mechanism. The impact of this development is facilitating the tax accounting process, tax fraudand thus increasing the tax outcome.To prove the research hypothesis, an electronic system was designed based on income tax report, estimation note of individuals, in additional to using Adobe Dreamweaver application to write PHP, HTML, Javascript, and CSS web languages to implement the proposed system. The research reached a set of conclusions, the most important of which is; not enough the communication methods between the Genera
... Show MoreIn this ˑwork, we present theˑ notion of the ˑgraph for a KU-semigroup as theˑundirected simple graphˑ with the vertices are the elementsˑ of and weˑˑstudy the ˑgraph ofˑ equivalence classesˑofˑ which is determinedˑ by theˑ definition equivalenceˑ relation ofˑ these verticesˑ, andˑ then some related ˑproperties areˑ given. Several examples are presented and some theorems are proved. Byˑ usingˑ the definitionˑ ofˑ isomorphicˑ graph, ˑwe showˑ thatˑ the graphˑ of equivalence ˑclasses ˑand the ˑgraphˑof ˑa KU-semigroup ˑ areˑ theˑ sameˑ, in special cases.