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 reflects the evidence of the Islamic Development Bank's role in building human and institutional capacities in Member States and assisting governments in achieving economic development. The Bank's activities in the area of capacity development are an important part in following up the economic developments, And help governments to build and formulate effective policies and institutions to implement more effective macro policies leading to better economic outcomes. It is therefore helpful to help Member States increase their resources, modernize their banking systems, establish effective legal frameworks and improve Reports on macroeconomic and financial statistics. The Bank has faced many challenges and risks tha
... Show MoreThis study aims to suggest an alternative to the use of quality agricultural soil in the brick industry (Iraq). The Late Miocene claystone bed in the Injana Formation in central Iraq was targeted through the study of 18 exposed sections that were sampled by using the trench sampling method. The claystones are characterized by quartz (36.4%) followed by calcite (32.8%), quartz (36.4%) feldspar (2.6%), gypsum (1.3%) and dolomite (0.7%), kaolinite (10.5%), illite (7.7%), chlorite (6.7%), palygorskite (6.0%) and montmorillonite (0.7%). New thermal mineral phases were formed at 950°C, including diopside (62.9%), quartz (18.4%), wollastonite (8.28%), akermanite (7.6%), Anorthite (6.25%), Nosean (4.9%), gehlenite (3.75%) and Lazurite (3.1
... Show MoreThe arise of Islam as a multidimensional changing phenomenon with its own revolutionary and comprehensive character was inherent with a lot of alterations in social aspects , and this is explicit particularly in the scope of urban life and town planning . Essentially, Islamic style of life has its own urban identity. The urbanization process in Islam has been developed across two integrated sides, the first one concerned on ideational and theoretical aspects , while the other associated with practice .Many urban centers emerged during the Islamic era since the erection of Basrah , the first Islamic town in the middle of the 7th. centaury. Some contemporary urban concepts , both environmental and social could be noticed in Islamic
... Show MoreThe purpose of this interview study was to explore teachers’ perceptions of Response to Intervention (RtI) implementation in their school. Particularly, the study explored teachers’ knowledge of RtI, teachers’ perceptions of RtI their intervention/instruction in school, and teachers’ suggestions of RtI implementation in their school. The study design was a qualitative interview in nature and data were collected from face-to-face interviews with four teachers in one school. The findings revealed that RtI means to identify students’ problems; the positive teachers’ perceptions of their implementation included: (a) students who demonstrate progress through RtI are those who receive private education services, (b) progress monito
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1- The degree of self-control of the educational counselors.
2- The level of work pressures that educational counselors are exposed to from their point of view.
3- The significance of the differences in the degree of self-control and work pressures according to the gender variable (male / female).
4- The relationship between self-control and work stress for the sample as a whole.
The current research was limited to educational counselors of both sexes in Anbar Governorate, Ramadi District, affiliated to the Anbar Education Directorate. The researcher adopted the steps of the relational descriptive approach to achieve the research objectives. The current research community consists of (100) m
... Show MoreA submerged weir is a hydraulic structure utilized to control flow in canals and rivers. Water scarcity is a persistent issue in Iraq, especially during the dry season when irrigation withdrawals reduce downstream water levels in canals (Water is lost from irrigation canals due to seepage, evaporation, and vegetation growth). The final section of the Bani Hassan Canal experiences significant drops in water surface (WS) levels, negatively impacting irrigation efficiency. This study addresses that gap by investigating the use of submerged weirs to enhance water distribution and raise WS in the final 6 km segment of the canal. A one-dimensional (1D) hydraulic mode
The study of the current study (to the concept of the aesthetics of the imagined in Iraqi ceramics (Saad Shaker) as a model for the study, as it represents one of the most important plastic arts that was characterized by renewal and modernity and its possession of many creative potentials. And by glazing, and the use of color oxides or by the creative act of borrowing the cultural heritage to turn it into a vocal piece of art for creation and innovation.
The researcher (Saad Shaker), being one of the first potters, his ceramics had a lot of development and semantic transmission, studying and decoding codes written in ceramic works. The current study included the theoretical framework in the first research (the philosophical beauty) an
Objective: To assess the nutritional status of hemodialysis patients.
Methodology: A descriptive quantitative cross sectional study was effectuated in hemodialysis centers from
February 2011 to September 2011. A purposive "non-probability" sample of (70) male and female hemodialysis
patients in al-Najaf al-Ashraf Governorate from those who have spent more than six months on maintenance
hemodialysis schedule. Data collected through using of a well-designed questionnaire consist of five parts, part
one consists of sociodemographic contain (9) items, and part two consists of medical data contain (8) items, and
part three consists of health and nutrition behavior contain (12) items plus (8) items of anthropometric
measur