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 current research included palynological study for nine ornamental cultivated species of Asteraceae family. The study included measurement the dimensions of pollen grains and there shape in polar view and equatorial view, sculpturing,colpi length and width, spines length and number of spines rows between colpiand exine thickness, the study showed variations in pollen grains characters forthe studied taxa
Abstract
In this study, modified organic solvent (organosolv) method was applied to remove high lignin content in the date palm fronds (type Al-Zahdi) which was taken from the Iraqi gardens. In modified organosolv, lignocellulosic material is fractionated into its constituents (lignin, cellulose and hemicellulose). In this process, solvent (organic)-water is brought into contact with the lignocellulosic biomass at high temperature, using stainless steel reactor (digester). Therefor; most of hemicellulose will remove from the biomass, while the solid residue (mainly cellulose) can be used in various industrial fields. Three variables were studied in this process: temperature, ratio of ethano
... Show MoreIn this work, an investigation for the dynamic analysis of thin composite cylindrical and spherical shells is presented. The analytical solution is based upon the higher order shear deformation theory of elastic shells from which the developed equations are derived to deal with orthotropic layers. This will cover the determination of the fundamental natural frequencies and mode shapes for simply supported composites cylindrical and spherical shells.
The analytical results obtained by using the derived equations were confirmed by the finite element technique using the well known Ansys package. The results have shown a good agreement with a maximum percentage of discrepancy, which gives a confidence o
... Show MoreThe current study sheds light on the measurement and estimation of the radioactivity of radionuclides (238U, 226Ra, 232Th, and 40k) in natural waters of different regions of Nineveh Governorate in Iraq.15 samples were collected from different sources of natural waters, where gamma-ray spectroscopy was used using NaI)TI) sodium iodide detector to determine the concentration of radioactivity in the samples. According to the results, the radioactivity concentration in the tested water sample were ranged from 0.36 ± 0.04-1.57 ± 0.09with an average value of 0.69 ± 0.06 Bq/l for 238U, and 2.9 ± 0.02-0.88 ± 0.03 with an average value of 0.65 ± 0.03 Bq/l for 226Ra Bq/l
... Show MoreTraditional programs and the tedious and financially costly processes they require are no longer the best choice for content makers. The continuous development and development have led to the emergence of competitive software that offers capabilities that are more suitable for aesthetic needs, as it breaks down stereotypical frameworks from the familiar to the unfamiliar to be more suitable for graphic subjects in terms of dealing with the requirements of the digital content industry. Video for communication platforms, as it has more advantages than traditional software and the flexibility and high quality it offers at the level of the final product, All of this contributed to supplementing the image with aesthetic employments with data
... Show MoreThe current research aims to identify the extent to which cognitive economics skills are included in the content of the chemistry textbook for the third intermediate grade, and the research sample was represented in the chemistry textbook for the third intermediate grade. A list of knowledge economy skills was prepared (6) main skills (basic skills, communication skills, thinking skills, work skills Group, information-gathering skill, behavioral skills (and (20) sub-skills) (reading, writing, operations, computer skills and employability, oral expression and written communication, dialogue, persuasion, influence and arousal, analysis, problem-solving, decision-making, suggestions and hypotheses and employing them. Controlling, directing
... Show MoreIraq is one of the most important countries in the world that has received its share of terrorist acts by the terrorist organization the Islamic State of Iraq and al-Sham (ISIS), which has caused instability, especially during the period of ISIS's control of seven Iraqi provinces (2014-2017). This stage has caused a decline in the levels of human and economic development and its inconsistency with the capabilities and needs of the Iraqi population. Therefore, this study aims to investigate the hypothesis that there is a close relationship between the decline in development in Iraq and the brutal practices of ISIS that it committed during his period of control over many Iraqi cities and regions. This study used several method
... Show MoreCorruption is a phenomenon that exists in all times and places, they appear in the developing countries and in developed countries, and in all political systems. And its repercussions and economic repercussions on the society in which it is rampant, and lead to the undermining of economic development and obstruction, is also working on increasing poverty and unemployment, as well as its role in the worsening of social problems, and political instability. And corruption is deviant behavior is illegal and contrary to the teachings of the religious and moral values. The emergence of this phenomenon is due to several reasons, including political, economic, social and cultura
... Show MoreThe aim of the research is to identify the imaginative thinking skills included in the content of the chemistry textbook for fifth-grade students in biological sciences at the preparatory stage, which is approved by the Ministry of Education, General Directorate of Curricula in the academic year 2020-2021. To achieve the objective of the study, the researcher depends on the previous studies in the field and content of imaginative thinking skills for preparing a list of skills that includes (3) essential skills and (11) sub-skills and (28) items related to all skills. The researcher adopted the analytical descriptive approach because of its appropriation of the goals of the research. Then the researcher analyzed the content of the book de
... Show MoreThe History of Multi Parties and its Effect on Political System in India