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.
This research seeks to attempt to reveal the intention of Al-Hafiz Al-Mazi from his market to hadiths from Imam Ahmad’s Musnad in his book “Masterpiece of Supervision in Knowing the Parties”, and researchers know that this book was classified by Al-Mazi to collect the parties to the six books: Sahih Al-Bukhari, Sahih Muslim, Sunan Abi Dawud, Jamea Al-Tirmidhi and Sunan Al-Nasa’i and Sunan Ibn Majah, in addition to some of the books ’authors’ books, and arranging them according to the Musnad, and it is not Musnad Ahmad from his condition, even if it is close to the arrangement of Mazi’s work, as he was a follower of that to the original owner Abu al-Qasim bin Asaker in his book “Supervising Knowledge of the Parties” in M
... Show MoreA Destructive Parenthood : The Problematic Motherhood in Selected Poems by Salvia Plath
In the light of what is witnessing in the advertising arena of new ways and methods in delivering advertising message to consumers by finding new outlets to communicate with them especially through social networking sites, which became the first choice of advertising companies in order to spread its goods and services. These companies now are relying gradually on celebrities to appear with their products and goods to drive the audience's attention towards them. The thesis aims to find out the attitudes of young people towards the the advertisements that show famous celebrities on social networking sites. The researcher used survey method which aims to record, analyze and interpret the phenomenon after collecting the necessa
... Show Moreسياسات الاتحاد الاوروبي والولايات المتحدة الامريكية تجاه ازمة الشرق الاوسط بعد الحادي عشر من ايلول
This study reveals important aspects of Ibn Tulun approach in this book through reading and scrutinizing the texts that had a direct or indirect relationship with this topic, as his study was not an easy thing, especially as it depends on the deduction of intellectual trends in his approach and his dealings with the texts of this topic In his directions and his architectural and service idea and highlighting its basic aspects as part of the plans of the Islamic city and its connection with the cultural heritage at the time.
Solar cells thin films were prepared using polyvinyl alcohol (PVA) as a thin film, with extract of natural pigment from local flower. A concentration of 0.1g/ml of polyvinyl alcohol solution in water was prepared for four samples, with various concentrations of plant pigment (0, 15, 25 and 50) % added to each of the four solutions separately for preparing (PVA with low concentrated dye , PVA with medium concentrated dye and PVA with high concentrated dye ) thin films respectively . Ultraviolet absorption regions were obtained by computerized UV-Visible (CECIL 2700). Optical properties including (absorbance, reflectance, absorption coefficient, energy gap and dielectric constant) via UV- Vis were tested, too. Fourier transform infra
... Show Moreيهدف البحث إلى معرفة ما هيه اخلاقيات مهنة العاملين في المكتبات وتحديث متطلباتهم الضرورية من المهنة لكي يسمو بأخلاقياتها ، وهل هذه الاخلاقيات متوافرة في العاملين في مكتباتنا الجامعية ضمن حدود الدراسة ؟ ومن ادوات جمع البيانات : استمارة بالاخلاقيات وزعت على مجموعة من الاساتذة و استبانة وزعت على من المكتبات الجامعية . وكان مجتمع الدراسة العاملون في المكتبات المركزية الأولى والثانية لجامعة بغداد والمكتبة المرك
... Show MoreThe verbal formula // i3-gal2 //is a commonly form in the written Sumerian economic texts, starting from the early dynastic period (2900-2372 BC), ending with the Ur III dynasty (2112-2004 BC). This formula has appeared either without infixes, or accompanied by infixes like / in-da-gal2/, corresponded in Akkadian the formula: ibaššu ,which is means "to found, to Storage ", As to the formula / da / come to indicate "to found with, to storage with--).