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.
Research Summary
This research is an attempt to explain the Qur’anic verses of the vision in the practical divine vision on the Day of Resurrection, and the legal texts narrated from the Companions regarding the vision of the Prophet, may God’s prayers and peace be upon him, regarding the vision of the Prophet, may God bless him and grant him peace, regarding the vision of the Prophet, may God’s prayers and peace be upon him, regarding the vision of the Prophet, may God bless him and grant him peace He was greeted with regard to vision, and he explained the two sayings of Ibn Abbas and Aisha on the same subject, including an area of conflict between them.
The escalating development of technology is one of the distinctive features of the communication environment in the field of sending and receiving satellite broadcasts of television channels in general and Iraqi satellite channels in particular, which contributed to the wide and rapid spread and reaching outside the drawn boundaries and bypassing even natural obstacles, and what is important in this is the communication content that these broadcasts Channels and its impact on the recipient due to the media, cultural, educational and entertainment content it provides, and in our research we will analyze the communication content of the Iraqi satellite channel by choosing one of its dialogue programs that coincided with the events of the l
... Show MoreToxic dyes are commonly discharged into waste waters and dyes are extensively used in the textile industry so it is necessary to find out efficient and eco-friendly method for treating waste waters resulting from industrial effluences. To achieve this aim the fungus Trichoderma sp. is employed into two lines: first line was self – immobilized fungal pellets in (Czapek – Dox medium) to adsorbs two dyes crystal violet, congo red by concentrations 0.01, 0.02, 0.03, 0.04, 0.05, 0.06 mg/L to both dyes, PH 2, room temperature with shaker in ( hrs.2,hrs.4,hrs.24) , by Uv- Visible spectrum . the removal efficiency of 0.05 mg/L crystal violet by Trichoderma sp was 96%. but there was no remova
... Show Moreشغلت نظرية العدل الإلهي بال الأديب العراقي القديم، مما جعلته يثير عبر نصوصه الأدبية كثير من التساؤلات حول عدالة الإلهة، التي يعبدها ويقدم لها الهدايا وتساؤلاته هذه دفعت بالباحث إلى اختيارها عنوانا لموضوعه، إلا أن الدراسة ستختصر على نصوص معينة، والسبب في ذلك أنها كانت الرائدة في هذا الجانب، وفي اللحظة التي ينتقي فيها العدل الإلهي وتتحول الإلهة إلى كلاب تلهث وراء غرائزها، ذهبنا وراء الأسباب التي قادت إلى فقد
... Show MoreIn the present work, the pollutants of the municipal wastewater are reduced using Chlorella vulgaris microalgae. The pollutants that were treated are: Total organic carbon (TOC), Chemical oxygen demand (COD), Nitrate (NO3), and Phosphate (PO4). Firstly, the treatment was achieved at atmospheric conditions (Temperature = 25oC), pH 7 with time (1 – 48 h). To study the effect of other microorganisms on the reduction of pollutants, sterilized wastewater and unsterilized wastewater were used for two types of packing (cylindrical plastic and cubic polystyrene) as well as algae's broth (without packing), where the microalgae are grown on the packing then transported to the wastewater for treatment. Th
... Show Moreهدفت الدراسة إلى الكشف عن العالقة بين الخبرات الصادمة والسلوك الفوضوي لدى طلبة المرحلة المتوسطة فضال عن التعرف على الفروق بين الطلبة في الخبرات الصادمة والسلوك الفوضوي على وفق متغير النوع )الذكور- اإلناث(، تألفت عينة الدراسة من )185( طالباً وطالبة، وتم تطبيق مقياسا الدراسة على العينة- مقياس الخبرة الصادمة ومقياس السلوك الفوضوي وهما )من إعداد الباحثان(، وقد أسفرت نتائج الدراسة عن: - إن طلبة المرحلة المتوسطة أظهر
... Show MoreThe study aims to identify the concept of empowering women from the point of view of experts in the Palestinian society, specifically in Gaza, as well as to explore the foundations of their formation of this concept. Additionally, the study seeks to clarify the most important challenges facing the empowerment of women in Palestinian society. The study used the design of a grounded theory that seeks to build the theory through deep analysis of the data, as qualitative data were collected through holding two focus groups and six in-depth interviews with the study sample, who were selected by the method of targeted sampling. The sample included (16) individuals (9 female experts, 7 male experts) holding academic and community leadership pos
... Show Moreهدفت الدراسة إلى الكشف عن العالقة بين الخبرات الصادمة والسلوك الفوضوي لدى طلبة المرحلة المتوسطة فضال عن التعرف على الفروق بين الطلبة في الخبرات الصادمة والسلوك الفوضوي على وفق متغير النوع )الذكور- اإلناث(، تألفت عينة الدراسة من )185( طالباً وطالبة، وتم تطبيق مقياسا الدراسة على العينة- مقياس الخبرة الصادمة ومقياس السلوك الفوضوي وهما )من إعداد الباحثان(، وقد أسفرت نتائج الدراسة عن: - إن طلبة المرحلة المتوسطة أظهر
... Show MoreSelf-driving automobiles are prominent in science and technology, which affect social and economic development. Deep learning (DL) is the most common area of study in artificial intelligence (AI). In recent years, deep learning-based solutions have been presented in the field of self-driving cars and have achieved outstanding results. Different studies investigated a variety of significant technologies for autonomous vehicles, including car navigation systems, path planning, environmental perception, as well as car control. End-to-end learning control directly converts sensory data into control commands in autonomous driving. This research aims to identify the most accurate pre-trained Deep Neural Network (DNN) for predicting the steerin
... Show MoreThis paper sheds light on aspects of environmental and climatic treatments in the groves mud existing in some Libyan oases. It reveals the architecture efforts and contributions to the adaptation of the construction and materials in order to organize the weather inside the building blocks to suit the nature of the human and his living in all seasons