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.
Mineral filler is one of important materials and affecting on properties and quality of asphalt mixtures .There are different types of mineral filler depended on cost and quality , the matter encourages us to achieve this study to evaluate hydrated lime filler effects on properties of asphalt mixes related with strength and durability. Conventional asphaltic concrete mixtures with Portland cement and soft sandstone fillers and mixtures modified with hydrated lime were evaluated for their fundamental engineering properties as defined by Marshall properties , index of retained strength , indirect tensile strength , permanent deformation characteristics , and fatigue resistance .A typical dense graded mixture employed in construction
... Show MoreHorizontal wells are of great interest to the petroleum industry today because they provide an attractive means for improving both production rate and recovery efficiency. The great improvements in drilling technology make it possible to drill horizontal wells with complex trajectories and extended for significant depths.
The aim of this paper is to present the design aspects of horizontal well. Well design aspects include selection of bit and casing sizes, detection of setting depths and drilling fluid density, casing, hydraulics, well profile, and construction of drillstring simulator. An Iraqi oil field (Ajeel field) is selected for designing horizontal well to increase the productivity. Short radius horizontal well is suggested fo
Morphologies of ceramic hollow fiber membranes prepared by a combined phase-inversion and sintering method were studied. The organic binder spinning solution containing suspended Al₂O₃ powders was spun to a hollow fiber precursor, which was then sintered at elevated temperatures( 300 ˚C, 1400 ˚C, 25 ˚C) in order to obtain the Al₂O₃ hollow fiber membranes. The spinning solution consisted of polyether sulfone (PES), N-methyl-2-pyrrolidone (NMP), which were used as polymer binder, solvent, respectively. The prepared Al₂O₃ hollow fiber membranes were characterized by a scanning electron microscope (SEM). It is believed that finger-like void formation in asymmetric ceramic membranes is initiated by hydrodynamically unstable vis
... Show MoreThis study was aimed to determine a phytotoxicity experiment with kerosene as a model of a total petroleum hydrocarbon (TPHs) as Kerosene pollutant at different concentrations (1% and 6%) with aeration rate (0 and 1 L/min) and retention time (7, 14, 21, 28 and 42 days), was carried out in a subsurface flow system (SSF) on the Barley wetland. It was noted that greatest elimination 95.7% recorded at 1% kerosene levels and aeration rate 1L / min after a period of 42 days of exposure; whereas it was 47% in the control test without plants. Furthermore, the percent of elimination efficiencies of hydrocarbons from the soil was ranged between 34.155%-95.7% for all TPHs (Kerosene) concentrations at aeration rate (0 and 1 L/min). The Barley c
... Show MoreBecause asceticism has a great impact on educating the human soul properly, according to what was mentioned in the Book and the Sunnah of the Prophet, and keeping it away from vices and what is devolving into it, and this world and its adornments keep the Muslim away from virtues and work with them in order to reach the Hereafter in which is the eternal bliss that God, peace be upon him, has prepared for the obedient. The two pious obedient ones. And because of the impact of this topic on the Islamic community and adorn it with good qualities. Likewise, I saw many Muslims who do not prefer the life of this world over the hereafter, and they began to fight over the world and enjoy its adornments, and they took pride in money, building, an
... Show MoreThe book gives details about the healing power of love
Although the profession of a marriage mediator is dominated by a social character, and it is also characterized by its practice in the midst of strict secrecy, because Eastern societies innately reject this method of searching for a life partner. The two parties play a prominent role of the will in the events of legal effects, and the obligations and rights owed by the contracting parties, which leads us to consider the agreement between the mediator and the one who wants to marry going to the purely contractual nature, and thus requires the correct legal adaptation on the contractual relationship that is achieved between the marriage mediator and his clients from Those who want to get married and therefore we will divide this research into
... Show MoreBasrah crude oil Vacuum residue 773+ K with specific gravity 1.107 and 4.87wt. % sulfur, was treated with hexane commercial fraction provided from Al-Taji Gas Company for preparing deasphaltened oil(DAO)suitable for hydrotreating process. Deasphaltening was carried out with 1h mixing time, 10ml:1g solvent to oil ratio and at room temperature. Hexane deasphaltened oil was hydrotreated on presulfied commercial Co-Mo/γ-Al2O3 catalyst in a trickle bed reactor. The hydrotreating process was carried out at temperature 660 K,LHSV 1.3 h^ –1, H2/oil ratio 300 l/l and constant pressure of 4MPa. The hydrotreated product was distillated under vacuum distillation unit. It is found that the mixture of 75% of vacuum residue with 25% anthracene satisfie
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