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 aims at evaluating the quality of the teaching skills of math teachers in junior high / scientific branch from their point of view.
The researchers prepared for this purpose a quality of teaching skills standards questionnaire, It consisted of 72 items distributed on four axis, The research sample was 200 teachers The researchers used statistical methods: the arithmetic mean, standard deviation, variance test, test Shiva , The results showed a statistically significance difference Attributed to the qualification variable in the second axis (Planning for teaching topics) And the absence of statistical difference function,
... Show MoreThe purpose of this paper is to introduce and study the concepts of fuzzy generalized open sets, fuzzy generalized closed sets, generalized continuous fuzzy proper functions and prove results about these concepts.
Irak Türk ağızları Azeri Türkçesinin bir uzantısı olarak değerlendirilir.Kerkük Türkçesiyle yazılan edebi ürünler, Irak Türkçesinin tamamını ifade etmek üzere kullanılmaktadır. Zamanın Eli divanı Kerkük Türkçesile yazılan bir eserdir. Bu yüzden bu divanı seçtik ve Irak Türkmen Türkçesi , Osmanlı Türkçesi ve Türkiye Türkçesi dilleri arasında karşılaştırmalı bir inceleme yaptık.
Bu araştırma, Irak Türkmen şairlerinden birisi sayılan Es’at Naib’in şiirleri üzerinde uygulamalı bir çalışmadanoluşmaktadır. Bu çalışmada adı geçen şairin “Zamanın Eli” Divanından bazışiirlerini önce yeni Türkçeye çevirdik vedaha sonra isim ç
... Show MoreThis paper try to shed light on one of interpretations of the prosody of Ibn Barry “Al-duraru l-lawāmi῾ fi maqra᾽i l-ImāmiNāfi῾” a famous prosody that students still study and spend time in memorize and understand it until this day. This interpretation is considered one of the simplest and appropriate to the nature of teaching in the early stages of education for students of Arabic in general. Also, we try very hard to extract the commons characteristics of this and other interpretation of the text we have, then effort a large text as an example of what we are going to say in conclusions.
Coagulation is the most important process in drinking water treatment. Alum coagulant increases the aluminum residuals, which have been linked in many studies to Alzheimer's disease. Therefore, it is very important to use it with the very optimal dose. In this paper, four sets of experiments were done to determine the relationship between raw water characteristics: turbidity, pH, alkalinity, temperature, and optimum doses of alum [ .14 O] to form a mathematical equation that could replace the need for jar test experiments. The experiments were performed under different conditions and under different seasonal circumstances. The optimal dose in every set was determined, and used to build a gene expression model (GEP). The models were co
... Show MoreGreatest travelers Muslims and Ousahm fame, called sheikh Rahalin to frequent roam in outlook, he spent twenty-eight years of his life in travel-related trips and successive, is Ibn Battuta, who wander in, as it was of adventurers who pushed curiosity to ride a lot of difficulties.
This study dealt with the presentation and documentation of the Iraqi women's participations in athletics in the Arab sports courses since the establishment of the Federation of Athletics in 1948 to 2017 as well as analysis of the results achieved for these participations and discuss the reasons for not participating in some of these courses and the researchers try to show the distinct role of Iraqi athletes, And their active contribution to these courses to represent the country as well as to promote the sports reality of Iraqi women compared to their Arab sisters, whose names have become a symbol of every Arab woman and therefore benefit from the experience of the Arab teams In athletics for women.
Fibroblast growth factors-23 (FGF-23) are a class of cell signaling proteins produced by macrophages. They have a range of roles, but they play a particularly important role in the development of animal cells, where they are essential for appropriate growth. Phosphate, which is found in the body as both organic and mineral phosphate, plays crucial roles in cell structure, communication, and metabolism. Most phosphate in the body resides in bone, teeth, and inside cells, with less than 1% circulating in serum. The aim of the study is to evaluate the levels of the Fibroblast Growth Factors-23 and phosphate and receiver operating characteristic (ROC) in acromegaly patients against healthy control. A case control study Fibroblast Growth Fact
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The problem of research on the study of political debate programs in the Iraqi satellite channels, in the "People decide" program by Afaq channel and " electoral competition " by Fallujah channel), and its importance for the community and researchers in the scientific field, as new programs to enter the Iraqi media after we have been the world media a lot in this area at the academic and practical levels (The field), and seeks to find out what the technical construction of the programs of political debates in Iraqi satellite channels and methods of construction and methods of employment used by the technical elements in the presentation of the programs and The study adopted the surve |