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.
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Obliquely deposited (70o) Bi, Sb, and Bi-Sb alloy thin films have been prepared by thermal
resistive technique. Structural properties of these films were studied using XRD. Their resistance and
voltage responsivity for Nd:YAG and CO2 laser pulses have been recorded as function of operating
temperature between 10 oC and 120 oC. It was found that the maximum responsivity for these detectors
can be obtained at 75 oC. On the other hand, the dependence of responsivity on the width of detectors was
investigated.
The accountants are preparing the financial statements under the Monetary Unit Stability Assumption without taking into consideration the changement of prices for the monetary unit. The income statement accounts containing different items of expenses and revenues. These items are not paid or obtained at one date, because the value of monetary unit is changing from one date to another , also the financial position contains different items of current and fixed assets, also contains different items of long-term liabilities and ownership rights, the continuity of applying historical cost principle will make the financial statements misleading, The adoption of financial analyst of these statements will affects
... Show MoreThe study aimed to investigate the employment of electronic supervision applications in developing the teaching performance of teachers in Oman. Based on the qualitative method and the study population consisted of all the teachers of the first cycle in the Governorate of Muscat. The study sample amounted to 24 female teachers. The interview was used as a tool for data collection. The study reached several results, including: There are difficulties in employing electronic supervision applications, which are weak network, density of curricula, lack of experience in applying technology, and the large number of tasks assigned to the teacher. These difficulties can also be overcome by strengthening the network, training teachers, reducing th
... Show MoreBackground: The study was designed to evaluate the effect of local application of exogenous VEGF/collagen I separately and as a combination in socket healing. Sixty male Albino Wistar rats were subjected for a surgical tooth extraction of upper 1st molar of both sides (right side was considered as experimental site, while left be the control one, treated with 1µL of normal saline). The rats were scarified at 3, 7, 14, 28 days post extraction. Socket healing was histologically examined with immunohistochemistochemical localization of ALP&FGF2. Materials and Method: Sixty male Albino Wistar rats were subjected for a surgical tooth extraction of upper 1stmolar of both sides (right side was considered as experimental site, while left be the
... Show MoreThis study was conducted in the botanical garden, Department of biology, College of Science / Mustansiriyah University in spring season, where the starts from (15 February to 15 March, 2019). Under the natural environmental conditions in the greenhouse in order to evaluate the effectiveness of some plant extracts as a promoter for rooting the apical stem cutting of rosemary plants at different concentrations compared with the IBA growth regulator. Plant extracts are Parsley (Petroselinum crispum), Dill (Anethum graveolens) and date palm fruits (Phoenix dactylifera) were used with concentrations (0, 1.25, 2.5 g / l). The IBA concentration was (100 mg / L) with dipping time 24 hour for all treatments. The following measurements were taken aft
... Show MoreThe monogenean Gyrodactylus lavareti Malmberg, 1957 is recorded here in the present study for the first time in Iraq from gills of the common carp Cyprinus carpio. This is the twentieth gyrodactylid species to be recorded from fishes of Iraq. The description and measurements of this parasite as well as its illustration were given.
The present study aims to identify the effectiveness of deductive group patterns in developing the creative thinking of second-intermediate-grade pupils in history discipline. The current null hypothesis has been investigated: There are no statistically significant differences at (0.05) between the scores mean of the experimental group pupils who were taught according to the deductive group pattern and the scores mean of the control group pupils who were taught according to traditional method in creative thinking testing. the study sample was divided into two groups: an experimental group of (30) female students and a control group of (31) female students. The two groups are equalized based on the variables of age, the scores of the firs
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