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.
Numerous drilling additives and materials are used continuously because they are necessary to support and give the required properties of the drilling fluid so that to ensure the stability of the borehole. This paper aspires to evaluate the rheological properties of bentonite (montmorillonite) Trefawey as an alternative to using commercial bentonite. Monitoring and evaluating of the rheological and filtration properties were prepared. This exertion aims to focus on the effect of hematite, and barite on the rheological properties of the three aforementioned bentonite types. An improvement in the rheological properties of bentonite (montmorillonite). Trefawey was observed after adding the previous heavy materials. Hematite has by some
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يعد البيت المكان الاجتماعي الأول الذي تبنى فيه الصحة النفسية لدى الفرد منذ بداية حياته كطفل في ظل أسرته ، إلا أن الروضة تمتلك على الرغم من ذلك أثراً تكوينياً مهماٌ في حياة الطفل وعلى شخصيته ، والتي لا يمكن ان يقلُّ عن أثر الايجابي للبيت ؛ ذلك أن المفهوم الجديد لدور الروضة لا يقتصر بمجرد كونها مكانًا تقوم فيها المعلمة بتزويد الاطفال بالمعر
... Show MoreThe bacterial contamination of lipsticks and face cream may become a great important matter in the medical laboratories. The present study was designed to determine the types of bacterial contamination in the face cream and lipsticks of undergraduate students. Also, the study aimed to determine the sensitivity of the isolated bacteria against many antibacterial agents. The study included 190 swabs samples from 190 face cream and lipsticks samples of the females’ students from five departments in the Medical Technology Institute, Almansour, Middle Technical University were collected in February 2018. The swab samples were collected with sterile condition and cultured on enriched Blood agar and MacConkey agar. Serial dilutions were made up
... Show MoreThe ground pearls, Porphyrophora tritici (Bod.) is a new insect pest on wheat recorded for
the first time from Mousl Province, North of Iraq.
Guanine has a variety of roles in chemistry, from its basic function in the storing and transferring genetic information to its usages in synthetic chemistry and other fields. Because of its distinct structure and biological importance, it is a fundamental component of contemporary study in organic chemistry and molecular biology. In this review, we focused on covering the synthetic pathways of various derivatives of guanine from the year 2000 until the present. As a result of the guanine molecule containing multiple functional groups, this gives us the ability to prepare several guanines such as O6-alkylating guanines, O6-benzylguanines, 8-aza-O6-benzylguanines, 9-substituted guanines, guanine-azo derivatives, guanine Schiff bases, guanin
... Show MoreBackground:Periodontal diseases and dental caries are the most common oral diseases, but they can be adequately prevented by adopting a specific health behavior and plaque control.The study was carried out to determine and compare oral health status; it included both caries experience, gingival health and oral hygiene behavior betweenfirst and fifth yearsof Al-Mustansiriyahdental students. Materials and methods: Total sample of the study consisted of 50 students at first year (25 males, 25 females)and 60 students at fifth year (30 males, 30 females). Plaque andgingival indices,dental caries indices (DMFS and DMFT) wererecorded to evaluateoral health status for each student. Further questionnaires were given to evaluate different oral hyg
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