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.
Abstract:
Al-Marba'aniyah, which is a long cold wave, was defined by ancient
Iraqis. It represents the coldest days in Iraq. In this research paper, a new
scale was put to define it. It shows that the period between the minimum
temperature degree recoded in December and the minimum temperature
degree recorded in January is considered to be the period of Al-Marba'aniyah.
The research concluded that Al-Marba'aniyah is unsteady and it changes in
the days of its occurrence. It was also concluded that the dates of the
beginning and the end of Al-Marba'aniyah are unsteady, too. Moreover, it was
found out that each of the Siberian high, European high, and finally the
subtropical high are the responsible systems for
Background: Data on the impact of neonatal and total pediatric admissions volume on neonatal mortality are sparse. Objectives: This study is done to estimate the neonatal mortality in relation to neonatal admissions and to total hospital admissions in Al-Alwyia Pediatric Teaching Hospital through years 2005-2012 Type of the study: A retrospective study.Methods: statistical records of all cases admitted to APTH were studied during 2005-2012.Results: Neonatal mortality decreased to the nadir at last year of study period (2012) and reached 6.1% of neonatal admissions compared to 2005 level which was 9.7 %. Mortality rate among premature and low birth weight (LBW) infants decreased also. The study also reveals that neonatal mortality constit
... Show MoreBackground: Cluster of differentiation 14 (CD14) is a serum/cell surface glycoprotein; and it is a pattern recognition receptor. CD14 expressed on the surface of various cells, or it found soluble in saliva and other body fluids. It has been proposed that soluble CD14 (sCD14) may play a protective role by controlling Gram negative bacterial infections through its capacity to bind lipopolysaccharide. This study was conducted to assess the level of soluble CD14 in saliva of patients with different periodontal diseases and healthy subjects and determine its correlation with clinical periodontal parameters. Materials & Methods: A total of 80 subjects, age ranged (25-50) years old, divided into three main groups, group ? consisted of 45 chronic
... Show MoreIn this research, we studied the multiple linear regression models for two variables in the presence of the autocorrelation problem for the error term observations and when the error is distributed with general logistic distribution. The auto regression model is involved in the studying and analyzing of the relationship between the variables, and through this relationship, the forecasting is completed with the variables as values. A simulation technique is used for comparison methods depending on the mean square error criteria in where the estimation methods that were used are (Generalized Least Squares, M Robust, and Laplace), and for different sizes of samples (20, 40, 60, 80, 100, 120). The M robust method is demonstrated the best metho
... Show MoreThis research aims to identify the impact of the selective model in acquiring the concepts of Kurdish grammar among female students in the eighth grade, and to achieve the goal of research, the researcher selected the experimental design with partial control and dimensional testing; the sample includes basic schools in the Chim district of Chamal/ Sulaymaniyah and randomly selected the basic school (Maha Bad) to be the field of application of the experiment and the random drawing method was chosen: two out of three sections and the number of students of the two sections is (75) students; section (C) represents the experimental group that studied the rules according to the selective model and its number is (37) students, while secti
... Show MoreIn this work, lanthanium (III) complexes were synthesized using by Schiff base ligand (L) derived from benzaldehyde and o-aminoaniline with five amino acids (AA) from glycine (Gly), L-alanine (Ala), L-valine (Val), L-asparagine (Asp) and DL- phenylalanine (Phe). The Schiff base ligand has been characterized by elemental analysis, (MASS, FTIR, 1HNMR, 13CNMR, UV-VIS) electronic spectra. The structures of the new complexes have been described of analysis of elements, molar conductivity, (UV-Vis electronic, FTIR, mass) spectra also magnetic moment. The molar conductivity values of the complexes indicat this every of complexes are electrolytes and other analytical studies reveal octahedral geometry for La (III) ion. The Schiff base ligand, five
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The research aims to build an integrated frame of knowledge for the basic research topics, represented by (assimilation of knowledge, strategic clarity) and their basic variables, by examining the most important scientific propositions on these topics in administrative thought, and framing the knowledge contained in them, in a serious attempt to provide appropriate answers to questions The research dilemma, and the research was applied in the Iraqi Airways Company, whose number is (1200) employees, and the descriptive and analytical approach was adopted in conducting the research. A valid form for statistical analysis, i.e., with a retrieval rate of (92%). The two researchers used the (SPSS & AMOS) program for
... Show Moremixtures of cyclohexane + n-decane and cyclohexane + 1-pentanol have been measured at 298.15, 308.15, 318.15, and 328.15 K over the whole mole fraction range. From these results, excess molar volumes, VE , have been calculated and fitted to the Flory equations. The VE values are negative and positive over the whole mole fraction range and at all temperatures. The excess refractive indices nE and excess viscosities ?E have been calculated from experimental refractive indices and viscosity measurements at different temperature and fitted to the mixing rules equations and Heric – Coursey equation respectively to predict theoretical refractive indices, we found good agreement between them for binary mixtures in this study. The variation of th
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