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 sciences related to the Book of God are many, and the benefits of every science in it are abundant, and among those sciences is the science of readings, which is for the sake of science and the most honorable, due to its strong attachment to the Book of God Almighty. From this care, and aims to show the attention of scholars to the science of readings in general and the scholars of the fifth century in particular, as the literature on it abounded until it became the principal for those who came after them.
The research consists of an introduction that includes the objectives of the research, the reasons for choosing it, previous studies, research questions, and research terms, then a preface dealing with the im
... Show MoreEach era has advantages in terms of innovation and development in form, technology, style, and design in ceramic vessels, both at the level of functional and aesthetic performance, so this study aimed to demonstrate the importance of geometrical foundations in the design structure of contemporary ceramic vessels, and also to reveal the constructive skills in The structure of the ceramic figure.
The researchers used the descriptive analytical approach to suit the nature of the study, and they described and analyzed the ceramic works in terms of geometric shape systems, elements and foundations of design in construction, formal diversity in the general design of ceramic vessels, and references and sources of artwork. In addition to th
Any design subject to a set of forces contributing to the establishment of relations working to strengthen the internal elements of the design; any imbalance in these elements can make a fragmented and weak design, thus preventing it from achieving the goal or performance. Poor performance can be attributed to various factors: the extent and function of the elements and principles in the design, realization of the idea, especially in fashion design.
Moreover, there are many aspects of a design that go into achieving the realization of the designer’s idea. The design utilizes a lot of stimulants by drawing attention to its design, which is consistent with the need for psychological and material individuals. In this research, we will
Research summary
Islam protects the environment and civilians in peace and war, and in international humanitarian law protection of the environment and civilians in international conflicts only. As for wars and internal conflicts, it is not within the jurisdiction of international humanitarian law. In Islamic law, the principles of protecting the environment and civilians are fixed in all wars and conflicts, whether internal or external, local. or international.
Islam laid down moral principles in war, including:
- Preserving the environment and avoiding corruption in the land by burning trees and killing animals unnecessarily.
- Not to be exposed to non-combatants, including women, boys, the elderly, the disa
... Show MoreBackground: Hypothyroidism is the most abundant thyroid disorder worldwide. For decades, levothyroxine was the main effective pharmacological treatment for hypothyroidism. A variety of factors can influence levothyroxine dose, such as genetic variations. Studying the impact of genetic polymorphisms on the administration of medications was risen remarkably. Different genetic variations were investigated that might affect levothyroxine dose requirements, especially the deiodinase enzymes. Deiodinase type 2 genetic polymorphisms’ impact on levothyroxine dose was studied in different populations.
Objective: To examine the association of the two single nucleotide polymorphism (SNP)s of deiodinase t
... Show MoreThe dose rate for bremsstrahlung radiation from beta particles with energy (1.710) MeV and (2.28) MeV which comes from (32P and 90Y) beta source respectively have been calculated through six materials (polyethylene, wood, aluminum, iron, tungsten and lead) for first shielding material with thickness (x=1) mm which are putting between beta sources and second shield (polyethylene, aluminum and lead) with thickness (1, 2 &4) mm have been calculated. The distance between beta source and second shield is constant (D=1) cm. This dose rate was found by program called Rad Pro Calculator (version 3.26). The results of dose rate of beta particles were plotted as a function to the atomic number (Z) for first shield materials for each
... Show MoreBackground: Coronary artery disease remains the main cause of death despite several preventive programs. Epicardial adipose tissue is a visceral fat depot of the heart located along the large coronary arteries and on the surface of ventricles and apex. Intima media thickness is commonly recognized as the initial stage in the development of atherosclerosis. The development of ultrasound machines, advances in echocardiographic devices and high resolution transducers facilitate comprehensive analysis of epicardial fat thickness (EFT) and carotid –intima media thickness (C-IMT).
Aim: To investigate the relationship of echocardiographic epicardial fat thickness (EFT) and carotid –intima media thickness (C-IMT) with the severity of coro
Abstract
This research aims to develop a unit as part of a sixth-grade Arabic language textbook and measure its effectiveness in the development of twenty-first-century skills of female students. The author adopted the experimental approach with a quasi-experimental design of the pre-post single-group. A list of the major skills was derived from the framework for the 21st-century skills of the mother tongue that was developed by the Partnership for 21st-Century Skills and reviewed and adjusted by some specialists. According to their views, the unit was developed. The study targeted 15 sub-skills falling under three main skills. The results of the study showed the effectiveness of the developed unit in the develo
... Show MoreBackground: Automobile spray painting is considered an occupation with a high risk of respiratory impairment and asthma. Exposure to organic solvents used for spraying might be of high risk for development of dysfunction in other organs.
Objective: The study was designed to evaluate the pulmonary and hepatic toxicity due to exposure of automobile painters to organic solvents in work places within the Baghdad governorate area.
Methods: Thirty cross sectional selected male workers employed in automobile body paint shops in two industrial areas within Baghdad city (Al-Sheikh Omar and Al-Rasheed camp regions) were recruited to the study during the period from March to May 2012. Thirty non-exposed students and employees in the college o