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.
We discussed the proper preparation, directing, and implementation of physical education lessons, and clarification of the duties that fall upon the physical education teacher in addition to his physical and skill duties, which is the duty of the physical education lesson. The problem of the research lies in the fact that interactive harmonic exercises are not implemented accurately by physical education teachers because they require great experience, exceptional efforts, and accuracy in performance. The research aims to identify the level of some physical and motor abilities and intelligence among students aged (9-10) years, and to know the effect of some harmonic exercises. Interactivity at the level of some physical and motor abi
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Purpose: The research attempts to Stand on the reality of the effective application of of strategic information systems in telecommunications companies in the Kurdistan Region, and what is the amount of the impact of such systems on promoting of Strategic Intelligence.
Design/Methodology/Approach: The Applied method has been used, In order to achieve the objectives of the research has been the development of a questionnaire prepared for this purpose and then distributed to (11) Company of Iraqi communications operating in Kurdistan Region companies, it has been used questionnaire to collect data in order to develop
... Show MoreIn this paper, a comparison of production and domestic consumption of Iraq's food industries within economic environment of a sample of countries is presented. Tracked by a number of variables, To extrapolate the reality of this industry in terms of its importance to individual consumption and importance on national economy, then, to find size and type of obstacles facing the industry in Iraq. Relationship was measured through use of quantitative methods and digital data in the comparison process. Results showed that the large growth in the size of the population in Iraq is not the first multiplier in the high consumption of processed food, but the increase in the per-capita income. The treatment takes several aspects related to the gene
... Show MoreThe adsorption of hexavalent chromium by preparing activated carbon from date seeds with zinc chloride as chemical activator and granular date seeds was studied in a batch system. The characteristics of date seeds and prepared activated carbon (ZAC) were determined and found to have a surface area 500.01 m2/g and 1050.01 m2/g , respectively and iodine number of 485.78 mg/g and 1012.91 mg/g, respectively. The effects of PH value (2-12), initial sorbate concentration(50-450mg/L), adsorbent weight (0.004-0.036g) and contact time (30-150 min) on the adsorption process were studied . For Cr(VI) adsorption on ZAC, at 120 min time contact, pH solution 2 and 0.02 adsorbent weight will ach
... Show MoreBackground: Enterococcus faecalis is emerging as an important endodontic pathogen, which can persist in the environment for extended periods after treatment and may cause endodontic failure. It is known to produce biofilms, a community of bacteria enclosed within a protective polymeric matrix. This study aimed to establish whether the biofilm formation by Enterococcus faecalis can be inhibited with steralium, co+steralium, and 5% sodium hypochlorite in the root surface environment. Materials and Methods: Extracted human teeth were biomechanically prepared, vertically sectioned, placed in the tissue culture wells exposing the root canal surface to E. faecalis to form a biofilm. At the end of the 3rd and 6th weeks, all groups were treated fo
... Show MoreA new ligand [4-chloro-N-(1,5-dimethyl-3-oxo-2-phenyl-2,3- dihydro-1H-pyrazol-4-ylcarb amothioyl) benzamide] (CAP) was synthesized by reaction of P-ChloroBenzoyl isothio cyanate with 4- aminoantipyrine,The ligand was characterized by micro elemental analysis C.H.N.S.,FT-IR,UV-Vis and1H13CNMR spectra, some transition metals complex of this ligand were prepared and characterized by FT-IR, UV-Vis spectra, conductivity measurements, magnetic susceptibility and atomic absorption. From the obtained results the molecular formula of all prepared complexes were [M(CAP)2(H2O)2]Cl2(M+2 =Mn, Co, Ni, Cu, Zn, Cd and Hg),the proposed geometrical structure for all complexes were octahedral
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This study aims to identify the degree to which the first cycle teachers use different feedback patterns in the E-learning system, to identify the differences in the degree of use according to specialization, teaching experience, and in-service training in the field of classroom assessment as well as the interaction between them. The study sample consisted of (350) female teachers of the first cycle in the governmental schools in Muscat Governorate for the academic year 2020/2021. The study used a questionnaire containing four different feedback patterns: reinforcement, informative, corrective, and interpretive feedback. The psychometric properties of the questionnaire were verified in terms of validity
... Show MoreThe removal of direct blue 71 dye from a prepared wastewater was studied employing batch electrocoagulation (EC) cell. The electrodes of aluminum were used. The influence of process variables which include initial pH (2.0-12.0), wastewater conductivity (0.8 -12.57) mS/cm , initial dye concentration (30 -210) mg/L, electrolysis time (3-12) min, current density (10-50) mA/cm2 were studied in order to maximize the color removal from wastewater. Experimental results showed that the color removal yield increases with increasing pH until pH 6.0 after that it decreased with increasing pH. The color removal increased with increasing current density, wastewater conductivity, electrolysis time, and decreased with increasing the concen
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