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.
<p>The objective of this paper is to study the dynamical behavior of an aquatic food web system. A mathematical model that includes nutrients, phytoplankton and zooplankton is proposed and analyzed. It is assumed that, the phytoplankton divided into two compartments namely toxic phytoplankton which produces a toxic substance as a defensive strategy against predation by zooplankton, and a nontoxic phytoplankton. All the feeding processes in this food web are formulating according to the Lotka-Volterra functional response. This model is represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global stability
... Show MoreThe subject of fear is one of the most important tasks that one should seek to find out the reasons behind it, and push it up with all its sound mental concepts.
The main reason for the lack of security and fear and disturbance in the world is to commit the legitimate violations that God warned us in his Holy Book as well as in the Sunnah of His Prophet (peace be upon him).
The talk about the causes of fear in the Koran is not limited to the word (fear) Fakk but came in different and varied methods such as (horror) and (awe) and (shares) and (narrow).
The development of thyroid gland in five developmental stages of common carp, Cyprinus carpio L. The thyroid originates from the pharyngeal floor as a median ventral keel in late embryos having four pairs of arches. It differentiates into profollicular aggergations and true follicles with flattened walls and empty lumina or with lumina filled with cotton waste-like material in three days-old elvers. Secretion of homogeneous eosinophilic colloid with a limited increase in the height of follicular wall is noted in five days-old elvers. In nine days-old individuals the follicles increase in size due to coallescence. The thyroid gland reaches its maximal activity as judged by its histology in one-two months-old individuals. The gland is of t
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Machining residual stresses correlate very closely with the cutting parameters and the tool geometries. This research work aims to investigate the effect of cutting speed, feed rate and depth of cut on the surface residual stress of steel AISI 1045 after face milling operation. After each milling test, the residual stress on the surface of the workpiece was measured by using X-ray diffraction technique. Design of Experiment (DOE) software was employed using the response surface methodology (RSM) technique with a central composite rotatable design to build a mathematical model to determine the relationship between the input variables and the response. The results showed that both
... Show MoreThe present study was conducted with a view to determine whether focal laser therapy result in visual recovery and regression of macular edema in patients with non proliferative diabetic retinopathy and maculopathy ,and whether combined focal and scatter laser therapy in patients with proliferative diabetic retinopathy and maculopathy results in visual recovery ,regression of macular edema and regression of the risk factors. In the present work, a frequency doubled Nd: YAG laser was used for the treatment of diabetic retinopathy. The study evaluates 41 eyes of 33 diabetic patients both with Insulin Dependent Diabetes Mellitus IDDM, (n=16) and Non Insulin Dependent Diabetes Mellitus NIDDM, (n=17) with diabetic retinopathy divided into two
... Show MoreIn this work four complexes of antimony were prepared ,Na[SbO(gly)2],Na[SbO(Asp)2],Na[SbO(Tyrosin)2], Na [SbO(phen alanin)2]. by reaction SbOCl with salts amino acids identifiefid these complexes by FTIR ,their conductivity was measured and also their biological activity against two types of bacteria was studied ,they were biologically active.
Objective: To find out the relationship between the bio-social aspect with cholelithiasis patients and
demographic characteristics in Baghdad city.
Methodology: A purposive (non-probability) sample of (100) patients, from (20-70) years old, who were
selected from patients who were admitted to hospital at preoperative stage, from Gastroenterology and
Hepatology Hospital, Baghdad Teaching Hospital, Al-Yarmook Teaching Hospital, Al-Karama Teaching
Hospital, Teaching Hospital. A descriptive study was carried out from 25th of June 2004 to the end of October
2004.
An assessment form was constructed for the purpose of the study. Test-retest reliability was employed through
computation of Pearson correlation coefficient.
In this paper had been studied the characterization of the nanocatalyst (NiO) Mesh electrodes. For fuel cell. The catalyst is prepared and also the electrodes The structural were studied through the analysis of X-ray diffraction of the prepared nanocatalyst for determining the yielding phase and atomic force microscope to identify the roughness of prepared catalyst surface, Use has been nanocatalyst led to optimization of cell voltage, current densities & power for a fuel cell.
This study dealt with IL-13 1024 (C/T) gene genotyping among patients with Thyroid goiter in Iraq. Forty blood samples from patients with Thyroid goiter were collected and compared with 30 healthy persons as controls. The genotyping results of IL-13 1024 (C/T) gene using ARMS-PCR revealed presence TT, CC and CT genotypes beside T and C alleles. The T allele and TT genotype frequency were higher in Thyroid goiter patients compared to the same genotype and allele in healthy persons (P = 0.060). These increasing results were related with increasing risk factor of Thyroid goiter (odds ratio [OR] 2.15; 95% confidence interval [CI] 0.99–71.4). No significant differences between genotypes for Thyroid goiter patients and controls were revealed by
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