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.
ملخص 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 communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.
Abstract:
The internal control is the tool through which it is possible to verify and ensure the implementation of tasks in accordance with the established plans and programs and to evaluate the level of performance that is implemented within the different companies.
A guarantee from the supplier with the absence of a specialized technical committee that follows up the stages of implementing the contract and disbursing all amounts of financial dues to the supplier before completing the implementation of the contract and overlooking the non-implementation of some clauses of the contract by the committee in charge of
... Show MoreThe effect of the concentration of the colloidal nanomaterial on their optical limiting behavior is reported in this paper. The colloids of sliver nanoparticles in deionized water were chemically prepared for the two concentrations (31 ppm and 11ppm). Two cw lasers (473 nm Blue DPSS laser and 532 nm Nd:YAG laser) are used to compare the optical limiting performance for the samples. UV–visible spectrophotometer, transmission electron microscope (TEM) and Fourier Transformation Infrared Spectrometer (FTIR) were used to obtain the characteristics of the sample. The nonlinear refractive index was calculated to be in the order of 10-9 cm2/W. The results demonstrate that the observed limiting response is significant for 532nm. In addition, t
... Show MoreAbstract
This research aims to evaluate the application of the inspectors general of global indicators offices according to the axles (leadership, strategy and planning, employees, partners and resources, process management) and through the assumption main research which states that (there is an application for global indicators to evaluate performance in the offices of the ministries under study) which are subdivided into five sub-hypotheses according to the classification and division of the five axes of the checklist.
The researchers have taken refuge in the process of assessing the performance of the check list which included global i
... Show MoreContemporary residential neighborhoods suffer from weak sustainability of urban residential environments as a result of the adoption of inefficient spatial organization at the neighborhood unit level. This resulted negative characteristics which affected the achievement of sustainable development plans for the residential environment that constitute the majority of the urban fabric of cities.
The physical affordances ,within the vocabulary of recent times,overcame the spiritual ones and affected the residential environment. Accordingly,the concept of space changed in contemporary residential areas through the dominance of the physical aspect (mass) on the symbolic aspect (space).The modern technology occupied an important level b
... Show MoreThe launch of the EU’s Eastern Partnership in 2009 intended to signal a new, elevated level of EU engagement with its Eastern neighborhood. Yet there remain several long-simmering and potentially destabilizing conflicts in the region, with which EU engagement thus far has been sporadic at best. The Union’s use of its Common Security and Defense Policy (CSDP) in the region and to help solve these disputes has been particularly ad hoc and inconsistent, wracked by inter-institutional incoherence and undermined by Member States’ inability to agree on a broad strategic vision for engagement with the area.
The three CSDP missions deployed to the region thus far have all suffered from this incoherence to various extents. In particu
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