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.
The Importance of Effort and its Impact in Building the Society in the Light of
the Holy Book and Sunna.
Thank for God and peace be upon Prophet Muhammad, His hose hold and
Companions.
This research is to refute a fault : that Islam as a religioncalls for laziness and
dependence and this in first, Second, to show the originality of the Islamic method in
building and construction.
This research Starts with an introduction in which I refer to the nature of the
Islamic method and its way of work in life: that it is a divine method that is achieved
by the effort of the people them selfves and not through a divine extraordinary power:
The research explains the shift in the peoples life who were addressed by this<
(Thimma) in Arabic means compact, and immunity. (People of Thimma) are the free non-Muslim people under Muslim rule. This includes Heavenly Religions people, i. e., Christian and Jews).
They have been called (People of Thimma) because they had paid (Jizyah: tribute) so they became safe for their souls, honor, properties at the custody of Muslims.
Islamic law had posed (Jizyah: tribute) upon the Jews and Christians who were living under Muslim rule as a reaction of not embracing Islam Faith against securing their rights and freedom.
Freedoms secured by Islam for the (People of Thimma) had been many, including the right of faith, not coercing them to be Muslim, the right to live, to possess properties, protect and secure them, the
This study aimed to develop an oral drug delivery system for gastro-retentive sustained drug release of baclofen by using a 3D printed capsular device since baclofen has a short half-life of 2.5 to 4 hours and has a narrow absorption window. Firstly sustained-release tablets of baclofen were formulated through the hot-melt extrusion of various thermoplastic polymers and direct compression of the extrudate, then a capsular device was designed and 3D printed to contain two air pockets to enable floating of the device and has four windows for drug release.
3D printing of the capsular device was done by an FDM printer using biodegradable PLA filament, and the sustained release tablets were inserted into the device to allow the medici
... Show MoreABSTRACT Background: Improving the properties of heat- cured and self-cured acrylic resin have been studied by many researchers. However, little studies concerned with visible light cured resin (VLCR) improved through addition of nanofiller are available. The purpose of this study was to evaluate some properties of (VLCR) after addition of SiO2 nanofiller. Materials and Methods: SiO2 nanofiller were added to (VLCR) tray material after being dissolved in tetrahydrofuran (THF) solvent. According to the pilot study 2% SiO2 nanofiller addition exhibited better properties than the other percentages (1%, 3%). The main study conducted involved (100) specimens divided into 5 groups according to the test included. (20) Specimens were selecte
... Show MoreThe grain hardness, wet and dry gluten contents, protein and ash contents are determined in grains from different cultivars of wheat which are important in food products, either which are present in raw materials or in final products. Wheat is also a very important food raw material, and flour as the final product of milling. The importance of knowing the physical and chemical properties of wheat and flour is due to the determination of quality and kind of flour which is produced after the milling process. In this work, some physical and chemical properties of different wheat cultivars are determined and the comparisons of these characteristics are performed in both wheat and flour. Uruq Wheat sample (W5) has the highest results when compar
... Show MoreBackground: One effective second-generation triptan for migraine attacks is sumatriptan. Following oral use, it has a 40% restricted bioavailability because of the first-pass metabolism. Aim: To develop the best intranasal Solusomes formula as a substitute that delivers into the brain directly, improving its bioavailability, and removing the first-pass outcome was the aim of this effort. Methodology: We developed solute formulations based on the Box-Behnken design and subsequently produced them via thin-film hydration. The quality by design technique was used to establish a correlation between the formulation parameters (Soluplus® and phosphatidylcholine (PC) concentrations) and signif¬icant quality powers (entrapment efficiency (
... Show MoreBackground. Colorectal cancer, ranking second place in global cancer mortality, arises from diverse causes. There is growing recognition of the substantial involvement of the epigenetic modifications of histones at the DNA level in the occurrence of CRC. Aim. To assess the expression of p53, HDAC1, and HDAC3 proteins in a cohort of CRC patients and to analyze potential relationship between their expression and the stages of CRC progression. Materials and Methods. The retrospective investigation was carried out on 95 paraffin-embedded CRC tissue samples. The expression of p53, HDAC1, and HDAC3 was assessed immunohistochemically. Results. Notably, the expression of the p53 protein in CRC tissue samples exhibited a prominent correlatio
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