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.
Most of the known cases of strong gravitational lensing involve multiple imaging of an active galactic nucleus. The properties of lensed active galactic nuclei make them promising systems for astrophysical applications of gravitational lensing. So we present a simple model for strong lensing in the gravitational lensed systems to calculate the age of four lensed galaxies, in the present work we take the freedman models with (k curvature index =0) Euclidian case, and the result show a good agreement with the other models.
Acinetobacter baumannii is highly adapted to hospital environments, causing persistent chronic infections due to its ability to form biofilms. In this work, the antibiofilm activity of AuNPs with a subMIC concentration of 9.34 μg/ml was investigated by the microtiter plate method against 80 clinical isolates of A. baumannii. The results revealed that the biofilm was significantly (P< 0.05) reduced by 48.2 – 82.1%.
This paper investigates the concept (α, β) derivation on semiring and extend a few results of this map on prime semiring. We establish the commutativity of prime semiring and investigate when (α, β) derivation becomes zero.
Some new heterocyclic compounds containing, cyclohexenone, indazole, isoxazoline, pyrmidine and pyrazoline ring system were prepared from chalcones (1a,b). The starting chalcones (1a,b) were obtained by a base catalyzed condensation of appropriately substituted benzaldehydes and 2-acetylbenzofuran. The reaction of the prepared chalcones with ethylacetoacetate/hydrazine hydrate, hydroxylamine hydrochloride, urea, thiourea, hydrazine hydrate, phenyl hydrazine or hydrazide derivatives gave the mentioned heterocycles. All synthesized compounds have been characterized by physical and spectral methods.
Iraqi kaolin was used for the preparation and characterization of NaY zeolite for biodiesel production via esterification reaction. Oleic acid was used usually as a typical simulated feedstock of high acid number for the esterification reaction.
The chemical composition for the prepared Nay zeolite is as following: (Ca2.6Na1.K0.1)(Al6.3Si17.7)O48.16H2O, the silica to alumina ratio in the prepared catalyst was found equal to 2.6 and Na2O content was 12.26 wt. %, with relative crystallinity equal to 147.4 % obtained by the X-ray diffraction. The surface area result shows that the prepared catalyst has 330 m2
... Show MoreNew complexes of M(II) with mixed ligand of 5-Chlorosalicylic acid (CSA) C7H5ClO3 as primary ligand and L- Valine (L-Val) C5H11NO2 as a secondary ligand were prepared and characterized by elemental analysis (C.H.N), UV., FT-IR, magnetic susceptibility, μeff (B.M) as well as the conductivity measurements (Λm ). In the complexes, the 5-chlorosalicylic acid is bidentate in all complexes coordinating through –OH- and –COO- groups; also L-Valine behaves as a bidentate ligand in all complexes through –NH2 and –COO- groups. These five mixed ligand complexes formulated as Na3[M(CSA)2(L-Val)]. The proposed molecular structure for all complexes is octahedral geometries. The synthesis complexes were tested in vitro for against four bacteria
... Show MoreIn this work, silver (Ag) self-metallization on a polyimide (PI) film was prepared through autocatalytic plating. PI films were prepared through the solution casting method, followed by etching with potassium hydroxide (KOH) solution, sensitization with tin chloride (SnCl2), and the use of palladium chloride (PdCl2) to activate the surface of PI. Energy-dispersive X-ray analysis (EDX) showed the highest peak in the (Ag) region and confirmed the presence of AgNPs. The diffraction peaks at 2θ = 38.2°, 44.5°, 64.6°, and 78.2° represented the 111, 200, 220, and 311 planes of Ag, respectively. The FT–IR an
... Show MoreMagnesium hydroxide was used as flame inhibitor to increased flame resistance for tires .Magnesium hydroxide was adding with (5%,10%) weight percents to rubber master batch of tire and then exposed the resulting material to a flame generated from gas torch with (10 mm) exposure distance . Method of measuring the surface temperature opposite to the flame was used to determine the heat transferred through tire material. The results were obtained shows enhanced flame resistance for tire by added magnesium hydroxide and this resistance increased by increasing hydroxide Percentage .
The wake potential and wake phenomena for swift proton in an amorphous carbon target were studied by utilising various dielectric function formalisms, including the Drude dielectric function, the Drude–Lorentz dielectric function and quantum dielectric function. The Drude model results exhibited a damped oscillatory behaviour in the longitudinal direction behind the projectile; the pattern of these oscillations decreases exponentially in the transverse direction. In addition, the wake potential extends slightly ahead of the projectile which also depends on the proton coordinate and velocity. The effect of electron binding on the wake potential, characterised by the ratio to 0.1, has been studied alongside the Drude–Lorentz dielectric
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