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 labeled research deal with (Entrepreneurship Organizations In the framework of strategic leadership practices: Field research in the Ministry of Oil), Search over the possibility of the influence of the practices of strategic leadership Which include
(Determine the strategic direction, The discovery of the fundamental estimators and maintain it, The development of the human capital, and Maintaining of an organizational culture influential, and Find a balanced regulatory Control) In a Entrepreneurship in its dimensions and its (innovation, risk, pre-emptive and independence) On group of heads of departments and authorities
... Show MoreThis study was designed to determine the percentage and the main causative agent causing bacteremia among children aged up to 12 years and complaining from different types of infections (Respiratory, intestinal, and urinary tract infection) in Baghdad. Results showed that the percentage of infection was 46.19 % the main causative agents were Enterobacteriaceae including (E.coli , Pseudomonas , Salmonella.typhi .Serratia , Enterobacter , Klebsiella )and other than Enterobacteriaceae which includes(Staph.aureus , Staph.epidermidis , Streptococcus.Pneumonia and ?-hemolytic streptococci ) .Regarding the age factor ,results showed that the highest infection rate was among the age group (1 day-12 month ) and (12 -36month ) (64.89%)an
... Show MoreIn order to understand the effect of (length of pile / diameter of pile) ratio on the load carrying capacity and settlement reduction behavior of piled raft resting on loose sand, laboratory model tests were conducted on small-scale models. The parameters studied were the effect of pile length and the number of piles. The load settlement behavior obtained from the tests has been validated by using 3-D finite element in ABAQUS program, was adopted to understand the load carrying response of piled raft and settlement reduction. The results of experimental work show that the increase in (Lp/dp) ratio led to increase in load carrying capacity by piled raft from (19.75 to 29.35%), (14.18 to 28.87%) and (0 to 16.49%) , the maximum load carr
... Show MoreThe present study aims to estimating the prevalence of autoimmune thyroid disorders in Iraqi infertile women with polycystic ovary syndrome (PCOS). Eighty-five Iraqi women, with age range (19-45) years, were divided into three groups; first group included 33 women with PCOS; second group included 30 women without PCOS; while third group included 22 fertile women as controls. The clinical data [age, body mass index (BMI), and menstrual status] have been recorded. Blood samples were collected to determine the levels of reproductive hormones [estradiol (E2), luteinizing hormone (LH), and follicle stimulating hormone (FSH)]; and thyroid hormones [triiodothyronine (T3) and thyroxin (T4)]. Also, autoimmune thyroid antibodies assessment h
... Show MoreThe mediation system is based on settling the dispute amicably through the intervention of a third party by bringing views closer away from the judiciary, which is an amicable way to settle disputes, which disputants resort to voluntarily, but some Western legislation has begun to impose resorting to mediation to settle disputes compulsorily, to take advantage of its advantages, get rid of the disadvantages of resorting to the judiciary in some disputes, and relieve pressure on the courts.
The main factors that make it possible to get the corrosion of reinforcing steel in concrete are chloride ions and the absorption of carbon dioxide from the environment, and each of them works with a mechanism which destroys the stable immunity of rebar in the concrete. In this work the effect of carbon dioxide content in the artificial concrete solution on the corrosion behavior of carbon steel reinforcing bar (CSRB) was studied, potentiostatically using CO2 stream gas at 6 level of concentrations; 0.03 to 2.0 weight percent, and the effect of rising electrolyte temperature was also followed in the range 20 to 50ᴼ C. Tafel plots and cyclic polarization procedures were obeyed to investigate the c
... Show MoreThe construction of highly safe and durable buildings that can bear accident damage risks including fire, earthquake, impact, and more, can be considered to be the most important goal in civil engineering technology. An experimental investigation was prepared to study the influence of adding various percentages 0%, 1.0%, and 1.5% of micro steel fiber volume fraction (Vf) to reactive powder concrete (RPC)—whose properties are compressive strength, splitting tensile strength, flexural strength, and absorbed energy—after the exposure to fire flame of various burning temperatures 300, 400, and 500 °C using gradual-, foam-, and sudden-cooling methods. The outcomes of this research proved that the maximum reduction in mechanical prop
... Show MoreThe current research aims to identify pictorial coding and its relationship to the aesthetic taste of art education students. The research community consisted of (10) plastic artworks, and (3) artworks were selected as a sample for analysis and decoding. With the aim of the research, the research tool was prepared as it consisted of an analysis form, and the researcher used statistical methods: Equation (Cooper) to find the percentage of agreement between the arbitrators and the equation (Scott) to calculate the validity of the tool, and the correlation coefficient (Pearson) to extract stability in the method of segmentation half. Shape formations and achieve encryption of the plastic image through decoding symbols, meanings, and the sig
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