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.
Background: Osteoarthritis is a complicated, chronic disorder of cartilage and bone, associated with homeostasis of bio-elements. The current study aims to assess the role of serum progranulin levels among Iraqi patients with knee osteoarthritis. Patients and Methods: The study encompassed 50 patients aged 52.50 ± 3.12 years (25 males and 25 females), admitted to the at the Baghdad Medical City through the period from November 2021 to March 2022. All individuals were identified by physicians in a Rheumatology and Rehabilitation Outpatient Clinic and the clinical data was collected along with the assess¬ment of biochemical parameters. Fasting serum glucose, lipid profile, calcium, magnesium, alkaline phosphatase, vitamin D3, and p
... Show MoreThis study carry’s out the correlation and the effect of two main variables, these variables are Job Satisfaction included six sub: wages - salaries and justice and yield, working conditions and services, pattern of supervision and the relationship with the manger, Relationship with colleagues, the content of the work and the variety of tasks, development and promotion opportunities available to an individual, and Organizational Performance included two sub variables: Efficiency, Effectiveness. This research was conducted using a questioner as a main tool, This questioner was distributed randomly to a research community composed of
... Show MoreThe use of external posttensioning technique for strengthening reinforced concrete girders has been considerably studied by many researchers worldwide. However, no available data are seen regarding strengthening full-scale composite prestressed concrete girders with external posttensioned technique under static and repeated loading. In this research, four full-scale composite prestressed I-shape girders of 16 m span were fabricated and tested under static and repeated loading up to failure. Accordingly, two girders were externally strengthened with posttensioned strands, while the other two girders were left without strengthening. The experimental tests include deflection, cracking load, ultimate strength and strains at midspan, a
... Show MoreThe coupling reaction between tryptamine and 8-hydroxyquinoline led to the formation of a new azo ligand. The synthesized ligand was characterized using CHN, FT-IR, UV-Vis, and NMR spectroscopic techniques. Complexes of the ligand with VO2+, Cr3+, Mn2+, and Mo6+ ions were prepared in a (1:2) ratio, with the general formula [M(L)2]. The obtained complexes were characterized using flame atomic absorption, CHN analysis, FT-IR, and UV-Vis spectroscopy, in addition to magnetic susceptibility and conductivity measurements. The findings suggest that the ligand functions as a bidentate, with the complexes exhibiting octahedral, square planar and square pyramidal geometries. All the complexes were identified as non-electrolytes. Their antioxidant ef
... Show MoreThe researchers wanted to make a new azo imidazole as a follow-up to their previous work. The ligand 4-[(2-Amino-4-phenylazo)-methyl]-cyclohexane carboxylic acid as a derivative of trans-4- (aminomethyl) cyclohexane carboxylic acid diazonium salt, and synthesis a series of its chelate complexes with metalions, characterized these compounds using a variety technique, including elemental analysis, FTIR, LC-Mass, 1H-NMRand UV-Vis spectral process as well TGA, conductivity and magnetic quantifications. Analytical data showed that the Co (II) complex out to 1:1 metal-ligand ratio with square planner and tetrahedral geometry, respectively while 1:2 metal-ligand ratio in the Cu(II), Cr(III), Mn(II), Zn(II), Ru(III)and Rh(III)complexes with octahed
... Show MoreWith a goal to identify, and ultimately removing from the oil fraction, the carcinogenic components, an oil fraction oil has been analyzed into a main three hydrocarbon groups, paraffins, aromatics, and polycyclic saturates. A multi-stage adsorption apparatus has been used. Four units of 300 g alumina each seems to be sufficient for removing the polynuclear aromatics from 75 g of an oil fraction boiling between 365-375 °C from Qurna crude oil. The usefulness of the ternary diagram for analyzing the oil fraction to the three hydrocarbons groups has been studied and verified. An experimentally based linear relationship of density and refractive index was established to enable of identifying the composition of an oil fraction using th
... Show MoreSouth Sudan is known by its tribal and racial variation .Tribal Perception represents the
procedure of dealings in Southern society .And that what make Sudan as a stable country that
suffer from divisions . Everybody wants to rule in spite of his inability and un qualification
which enables the establishment of an urbanized country .the frustration of the state in
handling the interior variety on religious, tribal and racial basis and contracting national
ideality in spared by shared ingredients between gathered groups in one state, all these reasons
make it hard to create a united national identity which is able to unite atheist and religious
parties together. Due to this ,the study is established to clarify the nat
The current study aimed to identify the morphological description and branches of the bronchial tree and lung for the weasel