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.
Break in the bond and its impact on the difference of scholars
Abstract
The intellectual capital an important variable in the equation of the success of seeking economic units to achieve a competitive advantage, since it is a real capital for economic unity it constitutes a strategic importance as the main source to achieve high profitability in the economic unit and highlights the importance of showing intellectual capital components of the main Represent of human capital and structural capital and relational capital, through effective and the prominent role played by intellectual capital within the economic unity in order to achieve a sustainable competitive advantage contribute to attracting investors with longer investment decision of the most important and difficult decisions ta
... Show MoreThis research was to determine the effect of rare earth metal (REM) on the as-cast microstructure of Mg-4Al alloy. The rare earth metal used here is Lanthanum to produce Mg-4Al-1.5La alloy. The microstructure was characterized by optical microscopy. The phases of this alloy were identified by X-ray diffraction. The microstructure of Mg-4Al consists of α-Mg and grain boundaries with precipitated phase particles. With the addition of Lanthanum, three distinct phases were identified in the X-ray diffraction patterns of the as cast Mg-4Al-1.5La: Mg, Al11La3, Al4La. The Mg17Al12 phase was not detected. The addition of Lanthanium increases the hardness and dec
... Show MoreIn this research a recent developed practical modeling technique is applied for the glucose regulation system identification. By using this technique a set of mathematical models is obtained instead of single one to compensate for the loss of information caused by the optimization technique in curve fitting algorithms, the diversity of members inside the single set is interpreted in term of restricted range of its parameters, also a diagnosis criteria is developed for detecting any disorder in the glucose regulation system by investigating the influence of variation of the parameters on the response of the system, this technique is applied in this research practically for 20 cases with association of National Center for
... Show MoreThe design, construction and investigation of experimental study of two compound parabolic concentrators (CPCs) with tubular absorber have been presented. The performance of CPCs have been evaluated by using outdoor experimental measurements including the instantaneous thermal efficiency. The two CPCs are tested instantly by holding them on a common structure. Many tests are conducted in the present work by truncating one of them in three different levels. For each truncation the acceptance half angle (θc) was changed. Geometrically, the acceptance half angle for standard CPC is (26o). For the truncation levels for the other CPC 1, 2 and 3 the acceptance half angle were 20o, 26o and 5
... Show MoreThis research includes a study of dezincification by corrosion from brass alloys in three types of media, which are acidic solution, basic and slat solution in different percentages. The study show the higher dezincification occurs in basic solution which decrease the fatigue properties where the fatigue properties are inversely proportional with dezincification.
Synthesis of 2-mercaptobenzothiazole (A1) is performed from the reaction of o-aminothiophenol and carbon disulfide CS2 in ethanol under basic condition. Compound (A1) is reacted with chloro acetyl chloride to give compound (A2). Hydrazide acid compound (A3) is obtained from the reaction of compound (A2) with hydrazine hydrate in ethanol under reflux in the presence of glacial acetic acid .The reaction of hydrazide acid compound (A3) with ethyl acetoacetate gives pyrazole compound (A4). The new hydrazone compound (A5) was prepared from the reaction of compound (A3) with benzaldehyde. Reaction of compound
... Show Moreفدهي قوس يف ةيداصتقلاا تادحولا ضعب يف نيرمثتسملا تارارق ىلع ءارضخلا ةبساحملا ريثأت ةسارد ىلا ثحبلا نم يلمعلا بناجلا تانايب عمج ىلع دامتعلااب ناثحابلا ماق ثحبلا فده قيقحتلو ، ةيلاملا قارولأل قارعلا نايبتسا ميمصت للاخ ىلا اهميدقتو يف ) نيرمثتسملاو , نييلخادلا نيققدملاو , نيبساحملاو , نييلاملا ءاردملا( ثحبلا ةنيع يف ةلجسملا تاكرشلا ضعب ةيلاملا قارولأل قارعلا قوس متو ثحبلا ناونعب قلعتت يتلا جئاتنلا جارخت
... Show Moreهدف البحث إلى معرفة تقويم الكفاءة الادارية لأعضاء اللجان المشرفة على التطبيقات التدريسية في كليات التربية بجامعة بغداد من وجهة نظر التدريسيين المشرفين عليها. اعتمد البحث المنهج الوصفي التحليلي. وتكون مجتمع البحث من (162) مشرفاً على التطبيقات التدريسية من كليات التربية/ جامعة بغداد، واختيرت عينة البحث بالطريقة العشوائية البسيطة، وبلغ عدد أفراد العينة (120) مشرفاً من الكليات آنفة الذكر. وتم بناء استبانة تضمنت (35)
... Show MoreThe research aims to measure the impact of managerial ability on income persistence for the industrial sector companies listed in the Iraqi Stock Exchange. The managers of these companies have managerial ability that may have an impact on achieving their objectives, setting their future policies and investing opportunities. Which may be reflected in many areas, including the level of profitability achieved and the possibility of continuity or sustainability? A model was used to measure managerial ability as well as a model to measure the income persistence in order to determine the relationship between them, The researchers found the absence of a statistically significant between managerial ability and the income persistence, which requi
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