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
This study aims at investigating the effectiveness of the cooperative inquiry strategy in developing the achievement and development of mathematical communication skills of elementary school students. To achieve this aim, the experimental method was utilized. The study sample consisted of an experimental group (n = 34) and a control group (n = 31), which were randomly selected from primary schools. A Teacher's Guide for teaching a unit entitled "Statistics and Graphic Representations" for the sixth elementary graders in the first semester were devised. A (30) multiple-choice item achievement test distributed at the levels of (recall, comprehension, and application), as well as an (18) item mathematical c
... Show Moresome ecological (physical and chemical varible) of water samples were studies monthly from December 2008 to May 2009 at two stations( St.1) Al - Chibayesh marsh and (St.2) Abu – Zirik marsh which are located in the south of Iraq . These variables included : Temperature, pH, EC, Dissolved oxygen , Total alkalinity, Nitrate, Sulphate, and phosphate, Si-SiO2 and Ca ,Mg, Cl, The marsh Considered as fresh water and alkaline. Abu-Zirik less than Al-Chibayesh.
Antibiotic resistance is the major growing threat facing the pharmacological treatment of bacterial infections. Therefore, bioprospecting the medicinal plants could provide potential sources for antimicrobial agents. Mimusops, the biggest and widely distributed plant genus of family Sapotaceae, is used in traditional medicines due to its promising pharmacological activities. This study was conducted to elucidate the antimicrobial effect of three unexplored Mimusops spp. (M. kummel, M. laurifolia and M. zeyheri). Furthermore, the mechanisms underlying such antibacterial activity were studied. The Mimusops leaf extracts revealed significant antibacterial activities against the five tested bacter
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The grammatical tools (the letters of meanings) are of great importance in understanding the meanings of the Arabic sentences,
This research is a simple attempt to show how our venerable scholars employed the meanings of these tools when they interpreted the linguistic evidence, that is, the grammatical structure largely depends on the tool in forming the meaning within the sentences and employing the meanings of these grammatical tools in explaining the linguistic evidence by clarifying their significance in the contexts of their use and effectiveness. Synthesis of the meanings of grammatical tools is an important tool in understanding the linguistic structure in order to reveal its meaning.
... Show MoreShallow foundations are usually used for structures with light to moderate loads where the soil underneath can carry them. In some cases, soil strength and/or other properties are not adequate and require improvement using one of the ground improvement techniques. Stone column is one of the common improvement techniques in which a column of stone is installed vertically in clayey soils. Stone columns are usually used to increase soil strength and to accelerate soil consolidation by acting as vertical drains. Many researches have been done to estimate the behavior of the improved soil. However, none of them considered the effect of stone column geometry on the behavior of the circular footing. In this research, finite ele
... Show MoreCervical carcinoma represent the second predominant cancer in female and there is a strong correlation between cervical cancer and the infection with high-risk types of HPV and expression the viral oncogenes. EMT is viewed as a vital advance in carcinoma development and ensuing metastasis. To evaluate correlation between the expression of Twist and HPV16 infection in a group of Iraqi patients with cervical carcinoma. A total of forty paraffin blocks included in this study which were divided into 30 sample of cervical cancer infected with HPV16and 10 sample of normal cervical tissues. The samples were subjected to immunohistochemical technique using Anti-Twist2 polyclonal antibody. The obtained data from this study indicate that majority of
... Show MoreThe results of previous scientific studies showed that knowledge is something and application is something else, that's why teachers' preparation programs focused, in the present time, on special standards for knowledge and performance, i.e., who has knowledge is not necessary able to apply it in his life or in his field of work, which led to the existence of a gap between knowledge and application. Based on that, those interested in (teachers' preparation) reconsidered their work evaluation, thus the concept of competency appeared at the end of the sixties of the past century to address the negative in teachers' preparation.
The following contains a number of competency features in teachers' preparation programs:
Teachers' effec
The aim of the study was extraction of arial part of Euphorbia cyathophora constituents with methanol and evaluate its effect on mitotic index and total chromosomal aberration bone marrow cell and spleen cell in mice 200 gm of E. cyathophora fine powder was defatted then extracted by cold maceration 80% ethanol for seven days. The extract was filtered and dried in a rotary evaporator then the dried extract was suspended with water and consecutively extracted using chloroform, ethyl acetate for each. The aqueous layer was then mixed with 100ml methanol. These fractions are dried under reduced pressure to obtain the dry extract. Twenty-four Albino mice were used for the experiment. The animals were divided into four groups: Gr
... Show MoreThe present study develops the sorption model for simulating the effects of pH and temperature on the uptake of cadmium from contaminated water using waste foundry sand (WFS) by allowing the variation of the maximum adsorption capacity and affinity constant. The presence of two acidic functional groups with the same or different affinity is the basis in the derivation of the two models; Model 1 and Model 2 respectively. The developed Bi-Langmuir model with different affinity (Model 2) has a remarkable ability in the description of process under consideration with coefficient of determination > 0.9838 and sum of squared error < 0.08514. This result is proved by FTIR test where the weak acids responsible of cadmium ions removal
... Show MoreBackground: Anti-oxidants are used as supplements to counteract the over production of free radicals in periodontal disease.Co-Q10 functions as an intercellular antioxidant by acting as a primary scavenger of free radicals (FRs) and reactive oxygen species (ROS), this study aimed to evaluate the effect of intra pocket application of perio Q gel (coenzyme Q10) alone and as adjunct to scaling and root planing on the periodontal clinical parameters in the treatment of patients with chronic periodontitis and compare the better improvement on the clinical periodontal parameters among different treatment modalities at 3 and 6 weeks. Materials and methods: A total of 323 sites with pocket depth (5-8) mm in patients with chronic periodontitis were
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