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.
Abstract
The research has discussed the public relations as dependent variable of its branch dimensions( confidence , commitment, control and satisfaction ) and the governmental service quality as independent variable of its branch dimensions (response, dependency, emphasis, tangibility and sympathy), and the research problem has represented by weakness of service quality presented to the customers dealing with company, which is observed via field co-existence of the researcher, where he observe that the quality presented in the company services, are inappropriate with the customers expectations level, also there is weakness of attention and recognition by the
This study was based on the determination of aphid species that infested Chrysanthemum sp. (Asterales, Asteraceae) in the middle of Iraq; five aphid species belong to subfamily Aphidinae were recorded: Aphis fabae Scopoli, 1763, Aphis gossypii Glover, 1877, Coloradoa rufomaculata (Wilson, 1908), Macrosiphoniella sanborni (Gillette, 1908) and Myzus persicae (Sulzer, 1776). A. gossypii was the most dominant species throughout the study period while M. persicae is the lesser species.
A summary of the main taxonomic characters is presented here and a pictorial key which was designed to separate aphi
... Show MoreIn this study, SnO2 nanoparticles were prepared from cost-low tin chloride (SnCl2.2H2O) and ethanol by adding ammonia solution by the sol-gel method, which is one of the lowest-cost and simplest techniques. The SnO2 nanoparticles were dried in a drying oven at a temperature of 70°C for 7 hours. After that, it burned in an oven at a temperature of 200°C for 24 hours. The structure, material, morphological, and optical properties of the synthesized SnO2 in nanoparticle sizes are studied utilizing X-ray diffraction. The Scherrer expression was used to compute nanoparticle sizes according to X-ray diffraction, and the results needed to be scrutinized more closely. The micro-strain indi
... Show MoreThe study aimed to evaluating the inhibitory activity of apigenin extracted from Salvia officinalis leaves on the growth of L20B cancer cell in vitro, and through two incubation periods; 48 and 72 hours. Accordingly, eight concentrations (1.56, 3.13, 6.25, 12.5, 25.0, 50.0, 100.0 and 200.0 micromol) of apigenin and similar concentrations of vitamin C and carbon tetrachloride (CCl4) were tested. The apigenin revealed its significant inhibitory potentials against the growth of L20B cell line, especially at the low concentrations (1.56, 3.13 and 6.25 micromol) and at 72 incubation period in comparison with vitamin C and CCl4.
Background: Separation and deboning of artificial teeth from denture bases present a major clinical and labortory problem which affect both the patient and the dentist. The optimal bond strength of artificial teeth with denture base reinforced with nanofillers and flexible denture bases and the effect of thermo cycling should be evaluated. This study was conducted to evaluate and compare the shear bond strength of artificial teeth (acrylic and porcelain) with denture bases reinforced by 5% Zirconium oxide nanofillers and flexible bases under the effect of different surface treatments and thermo cycling and comparing the results with conventional water bath cured denture bases. Material and methods: Two types of artificial teeth; acrylic and
... Show MoreThe study showed significant differences between the average weight lens and the average amount protein in the lens between that Kestrel Falco tinnunculus L. and the Collared Dove Streptopelia decaocto F. , also the study electrical migration of lens proteins having one bundle of crystalline –? in Kestrel compared with three bundles in Collared Dove, two bundles of crystalline – ? in both , and crystalline – ? appeared as one bundle in both birds.
In this study, concentrations of radon were measured for seventeen samples of soil distributed in three Sulphuric Spring, in addition to other regions as a background in Hit City in AL-Anbar Governorate. The radon concentrations in soil samples measured by using alpha-emitters registration that emits from radon (222Rn) in (CR-39) track detector. The concentrations values were calculated by a comparison with standard samples. The results show that the radon concentrations in first spring varies from (258.253- 347.762 Bq/m3), second spring (230.374-305.209 Bq/m3), third spring (292.002-336.023 Bq/m3) and the average radon concentration in other regions (187.821 Bq/m3). As a conclusion of the study radon concentration in Sulphuric Spring is r
... Show MoreThe Log-Logistic distribution is one of the important statistical distributions as it can be applied in many fields and biological experiments and other experiments, and its importance comes from the importance of determining the survival function of those experiments. The research will be summarized in making a comparison between the method of maximum likelihood and the method of least squares and the method of weighted least squares to estimate the parameters and survival function of the log-logistic distribution using the comparison criteria MSE, MAPE, IMSE, and this research was applied to real data for breast cancer patients. The results showed that the method of Maximum likelihood best in the case of estimating the paramete
... Show MoreThis study was conducted to test the effect of aqueous and alcoholic extracts for cyperus rotundus on the mitosis in tap roots of Allium cepa. the result of general an identical qualitative tests showed contains certain compounds that of crude aqueous and alcoholic extract, Used as five different concentrations of (10, 20.38, 56, 75) mg / ml for a period of four hours of treatment. After the chemical has been detected for some preliminary chemical compounds of the crude aqueous extract, while the alcoholic extract either phenol compound has been detected for phenols using several techniques included the use of thin layer chromatography TLC and measurement of disability factor RF and the degree of fusion and measurement of absorbance. The r
... Show Moreמחקר זה עוסק בנושא (העיירה היהודית) שטטל ביצירותיהם של שני סופרים עבריים שהתמקדו בביקורת בשטטל. וזה נחשב להגבלה או למכשול לפיתוחם של היהודים, אז זה התרחש ביצירותיהם והם נתנו תשומת לב רבה לזה –לפי דעתם- גם זה נחשב להיבט בהיסטוריה והחיים של היהודים באירופה.
סופרים עבריים רבים התעסקו בנושא השטטל שנהיתה לחומר ביצירותיהם. גם כן נהיתה אצל כמה מהם לשאלה חשובה, כי אם אנו מוצאים שיצירותיהם לא נטשו את האזכור
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