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.
formation constants for the conrdination of aniline pyridine dimethyl sulfoxide dimethyl formamide ethanol dimethylamine have been determined the cordination
This study assessed the advantage of using earthworms in combination with punch waste and nutrients in remediating drill cuttings contaminated with hydrocarbons. Analyses were performed on day 0, 7, 14, 21, and 28 of the experiment. Two hydrocarbon concentrations were used (20000 mg/kg and 40000 mg/kg) for three groups of earthworms number which were five, ten and twenty earthworms. After 28 days, the total petroleum hydrocarbon (TPH) concentration (20000 mg/kg) was reduced to 13200 mg/kg, 9800 mg/kg, and 6300 mg/kg in treatments with five, ten and twenty earthworms respectively. Also, TPH concentration (40000 mg/kg) was reduced to 22000 mg/kg, 10100 mg/kg, and 4200 mg/kg in treatments with the above number of earthworms respectively. The p
... Show MoreIn this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.
Marriage as a social case began Almighty God created Adam, peace be upon him then created from the rib Eve to be the first couple of human beings on the face of the earth and the formation of the first social family in the land, human and picked up this social reality through the generations, but in different shapes and purposes, but the mating process is one. So I got the divine religions and organized that life, especially in Islam, as explained every aspect of the life of the role and practice of marriage and had a large share in this organization and I got many Quranic verses and the Hadith.
With different civilizations, many of the marriage ceremony appeared in ancient societies take several forms of marriage.
But marriage and
Novel heterocyclic polyimide 5(a,b) have been synthesized based on polyacrylic backbone. The synthetic route start with nucleophilic substitution of 2-amino, or 4-amino, pyridine 1(a,b) to the polyacryloyl chloride afforded poly substituted amide 2(a,b). Another nucleophilic substitution were carried with adipoyl chloride to form polyimide chloride 3(a,b). Treatment of 3(a,b) with hydrazine hydrate afforded acid hydrazide polyimide 4(a,b), which upon cyclocondensation with carbon disulfide gave the target heterocyclic polyimide. The synthesized compounds were identified by spectroscopic methods: FT-IR, 1H-NMR and 13C-NMR.
Media theories and studies have provided many diligences on the concept of social media and the circle of influence, including the theory of social marketing which deals with how to promote ideas espoused by the elite in a society to become a recognized social value. The emergence of social networks provided a revolutionary breakthrough, taking the media to unprecedented horizons; and giving its users great opportunities to influence and move across borders without restrictions and censorship, except in a relatively limited manner. So, the emergence of social media has created channels of live broadcasting from its audience in a method of development that changes the essence of the known communication theories; and stops the monopoly of th
... Show MoreThis conducted research, (The Scientific Efforts of Ahmed Mustafa Al-Maraghi) deals with Al-Maraghi's life, birth, upbringing, characteristics, title, family and religion secter, as well as his general biography. And his relationship with scholars, his learning and teaching, and the introduction of the Muhammed Abdo School and the College of Dar Al Uloom, and finally the discussion of his scientific, social and political poin of view, as an interpreter of twentieths century, was appointed as the president of Al-Azhar and Ifta during the days of the royal era, and he studied at the College of Dar Al-Uloom
This research is based on the study of common praise in Mutanabbi and Ibn Hani Al-Andalusi as the main purpose in poetry poets, and balance between them;
The research was divided into two topics, presented by introductory introduction for the purpose of praise, and the concept of budget in Arab criticism, and then presented a brief overview of the lives of poets.
In the first section, I dealt with the common objectivity of the poets, such as the subject of sincerity in praise, hyperbole in the person of Mamdouh, and self-esteem when asked, in addition to the most common characteristics in t
... Show MorePolyaniline polymer has been prepared by chemical oxidation
polymerization method in laboratory successfully. The PANI and
(PVA+PVP) as a polymer blends in different percentage (30%, 50%,
70%) from Polyaniline was prepared. The sample was studies as
optical properties by UV-vis spectrophotometer at (400-700) nm.
The result of optical energy gap was 2.23 eV for pure (PVA+ PVP)
and with additive was increasing with increasing PANI concentration
to become (2.49 for 30% to 2.52 for 70%) PANI. The goal of this
project is prepare triple blend polymer and study the effect when add
conductive polymer (Polyaniline) on the optical properties and
calculate optical constant as energy gap, refractive index, dielectric
An investigation was conducted to study the concentration of hydrogen peroxide by vacuum distillation. The effect of the process variables (such as vacuum pressure, reflux ratio, time of distillation, and packing height of the column used in the distillation process) on the concentration of hydrogen peroxide were investigated. During the third stage of distillation (95 wt.%) concentration was obtained.
Box-Wilson central composite rotatable design is used to design the experimental work for the mentioned variables. It was found that the concentration of hydrogen peroxide increases with Increasing vacuum pressure, decreasing reflux ratio, increasing the time of distillation and increasing the packing height.
The second ord
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