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.
This paper deals with the preparation of new monomers and polymers which including heterocyclic unit. The diacid chlorides compounds [1-3] were prepared from the reaction of glutaric acid, adipic acid, terephthalic acid with thionyl chloride. Succinic acid reacted with ethanol to produce compound [4]. Compound [4] reacted with hydrazine hydrate to obtain succinic hydrazide [5].Compound [5] reaction with CS2 and KOH in absolute ethanol to produce compound [6].The polymers [7-12] have been created by reacting diacid chlorides compounds [1-3] with compound[5] or [6] in dry pyridine with some drops of DMF. The topology of produced compounds has characterized through their spectral and analytical data as in FT-IR spectra, Thermal analysis [DSC,
... Show MorePsychological aspects are a major influence and motivation factor in many cinematic and television works such as television series. There are many films that dealt with psychological issues through the personality affected by psychological projections and complexes that lead towards abnormal behavior and actions in most cases, so the researchers chose the title and the research problem was raised through the following question: What is the mechanism that fulfills a psychological role in the narrative film? The objectives of the research were to reveal the mechanism used to instill psychological contents in the feature film? As for the limits of the research, it was an intentional sample, and the researchers adopted the descriptive anal
... Show MoreThe tourism activity is one of the pillars on which the economy of any country is based , the importance of the tourism sector is reflected in its potential to become an effective development alternative in many countries, especially Iraq ,this has a direct impact on the national economy as an important source in attracting hard currency and eliminating unemployment. Adding the Iraqi Marshlands to the list of effects makes it contribute to diversification of sources of income and stimulating rest of the economic sectors, the potentials and qualifications possessed by Iraq in the field of tourism and monuments have a significant impact on the state budget if they were exploited optimally. The research aims at identifying the contr
... Show MoreThis study aims to develop a thermosensitive mucoadhesive periodontal in situ gel of secnidazole for local release of drug for treatment of periodontitis, in order to increase the drug residence time and to increase patient compliance while lowering the side effects of the drug.
Cold method was used to prepare 30 formulas of secnidazole periodontal in situ gel, using different concentrations of thermosensitive polymers (poloxamer407 alone or in combination with poloxamer 188) and methyl cellulose (MC ) or hydroxypropyl methylcellulose (HPMC K4M )in different concentrations used as mucoadhesive polymer and the resultant formulations were subjected to several tests such as gelation temperature GT, appearance and pH value. The fo
... Show MoreObjective: The objective of the present study was to design and optimize oral fast dissolving film (OFDF) of practically insoluble drug lafutidine in order to enhance bioavailability and patient compliance especially for a geriatric and unconscious patient who are suffering from difficulty in swallowing.Methods: The films were prepared by a solvent casting method using low-grade hydroxyl propyl methyl cellulose (HPMC E5), polyvinyl alcohol (PVA), and sodium carboxymethyl cellulose (SCMC) as film forming polymers. Polyethylene glycol 400 (PEG400), propylene glycol (PG) and glycerin were used as a plasticizer to enhance the film forming properties of the polymer. Tween 80 (1% solution) and poloxamer407 were used as a surfactant, citri
... Show MoreThe current study examined the effect of different sample sizes to detect the Item differential functioning (DIF). The study has used three different sizes of the samples (300, 500, 1000), as well as to test a component of twenty polytomous items, where each item has five categories. They were used Graded Response Model as a single polytomous item response theory model to estimate items and individuals’ parameters. The study has used the Mantel-Haenszel (MH) way to detect (DIF) through each case for the different samples. The results of the study showed the inverse relationship between the sample size and the number of items, which showed a differential performer.
The using of waste products as a recycled material was one of the most important studies for saving money and reduces the pollution. Mortar and concrete mixes with (10, 20 and 30)% of brick, glass and tile powder as replacement by weight of cement was investigated. The concrete mixes using brick or glass as 10%replacement of cement exhibited enhancement in compressive strength about (6, 4.7 and 2.0)% and (7.2, 5.6 and 2)% at age 7, 28 and 90 days respectively compared to reference mix. The 20% replacement of glass powder also showed an increase in the compressive strength up to (8, 6.3 and 4) %at age 7,28 and 90 days respectively compared to reference mix. Finally concrete mix using (10, 20 and 30) % tile powder as replacement of cement sho
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