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.
Praise be to God, and prayers and peace be upon our master Muhammad, the Messenger of God, and upon his family, companions, and those who are guided by his guidance.
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Our Islamic jurisprudence and its basic principles are fixed, namely: the Noble Qur’an, then the Prophet’s Sunnah, then consensus, then analogy. However, it is characteristic of what makes it developed to meet the requirements of renewed life, including: sent interests, custom, approval, blocking pretexts, changing times. That is why it went through different stages, growth, brilliance, stagnation and endowment; Therefore, many scholars of Islamic jurisprudence divided its stages into four sections: the stage of inf
... Show MoreThis work contain many steps starting from esterification of isophthalic acid to yield diester compound [I] which was converted to their acid hydrazide [II], then the later compound reacted with ethylacetoacetate to yield pyrazol-5-one compound [III]. Afterword added acetyl chloride to give the compound [IV], thereaction of this compound with theiosemicarbazide ledto produce a new carbothioamide compound [V], Which was reacted with ethyl chloro acetate to yield thethioxoimidazolidin compound [VI]. The condensation reaction of this compound with different substituted aldehyde give new alkene derivatives[VII]a-d. The synthesized compounds were characterized by melting points , FT-IR ,1H-NMR and Mass spectroscopy .
A new compounds of 2,4-substituted-1,3- thiazole containing amines [I] and [II], Schiff bases [IV] and [V], amides [VI]-[X],esters [XI] - [XIII], thiazolidinones [XIV]-[XVIII] and 1,3-oxazepines [XIX]-[XXV] were Synthesized and characterized by melting points, FTIR spectroscopy, elemental analysis, 1HNMR,13CNMR, dept135and Mass spectroscopy. The liquid crystalline properties of the synthesized compounds were verified by using hot-stage polarizing optical microscopy (POM) and differential scanning calorimeter (DSC). The compound [I] was found to be nematic textures (N). The first series of this study [II]n display only enantiotropic nematic phase when n=1-5 while the compounds with n =6-8 display two mesophasese smectic C(SmC) and nematic ph
... Show MoreMechanism of Arbitration in the Stock Exchange Disputes
Objectives To quantify the reproducibility of the drill calibration process in dynamic navigation guided placement of dental implants and to identify the human factors that could affect the precision of this process in order to improve the overall implant placement accuracy. Methods A set of six drills and four implants were calibrated by three operators following the standard calibration process of NaviDent® (ClaroNav Inc.). The reproducibility of the position of each tip of a drill or implant was calculated in relation to the pre-planned implants’ entry and apex positions. Intra- and inter-operator reliabilities were reported. The effects of the drill length and shape on the reproducibility of the calibration process were also investig
... Show MoreHydrodynamics is the interpretation of subsurface fluids and pressures to explain and predict hydrocarbon occurrence and trapping. Different models of fluid flow and hydrocarbon entrapments were constructed for the Mishrif Formation in (Rumaila South RU, Rumaila North R, West Qurna WQ, Majnon MJ, and ZubairZB) oilfields in Basra, southern Iraq. The dynamic flow within the oil reservoir was analyzed by measuring the specific gravity, hydrostatic pressure, hydrodynamic pressure, pressure gradient, salinity and hydraulic head. Fluid saturation in the pore space, hydrodynamic parameters, density, permeability and buoyancy influence fluid flow. The hydrodynamic model indicates that the oil fields are non-isolated reservoirs with a unifor
... Show MoreThis paper presents the application of nonlinear finite element models in the analysis of dapped-ends pre-stressed reinforced concrete girders under static loading by using ANSYS software. The girder dimensions are (4.90 m span, 0.40 m depth, 0.20 m width, 0.20 m nib depth, and 0.10 m nib length) and the parameters considered in this research are the pre-stress effect, and strand profile (straight and draped).
The numerical results are compared with the experimental results of the same girders. The comparisons are carried out in terms of initial prestress effect, load- deflection curve, and failure load. Good agreement was obtained between the analytical and experimental results. Even that, the
... Show MoreThis study aims to investigate the behavior and strength of self-compacted ferrocement slabs under punching shear load. Experimental results of thirteen square ferrocement slabs of 500×500 mm simply supported on all edges are presented. The main parameters investigated include the volume fraction of reinforcement, slab thickness and size of load-bearing plate. The load deflection and cracking characteristics of the tested slabs are studied and compared. The test results showed that the volume fraction of wire mesh has significant effect on both ultimate load and displacement. The increase of slab thickness leads to decrease in deflection values and increase in stiffness of slabs. Both ductility and stiffness increase as the
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