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
Objectives: To find out the association between enhancing learning needs and demographic characteristic of (gender, education level and age).
Methods: This study was conducted on purposive sample was selected to obtain representative and accurate data consisting of (90) patients who are in a peroid of recovering from myocardial infarction at Missan Center for Cardiac Diseases and Surgery, (10) patients were excluded for the pilot study, Data were analyzed using descriptive statistical data analysis approach of frequency, percentage, and analysis of variance (ANOVA).
Results: The study finding shows, there was sign
... Show MoreThe research aims to identify the effect of the training program that is based on integrating futuristic thinking skills with classroom interaction patterns on mathematics teachers in order to provide their students with creative solution skills. The research sample consisted of 31teachers (15 teachers for the experimental group and 16 for the control groups). The researcher developed a measure for the academic self-efficacy consisting of (39) items. Its validity, reliability, coefficient of difficulty and discriminatory power were estimated. To analyze the findings, the researcher adopted the Mann-Whitney (U) test and the effect size, and the findings were as follows: There is a statistically significant difference at the significance leve
... Show MoreGod Almighty put in his great book secrets that do not end, and wonders that do not expire, for he is the one from which the scholars are not satisfied, and he does not create due to the multitude of response, and it is the comprehensive and inhibitory book that God conceals to the worlds, and he challenged the two heavyweights to come up with something like it.
At all times, issues arise in the Noble Qur’an that fit the needs of the people of that time and their culture, for it is an eternal book, characterized by the ability to give, extend and respond to addressing the problems of the age and its variables, when the Arabs had little luck at the time of the message’s descent from the scientific culture, and their proficienc
... Show MoreTwo Schiff bases, namely, 3-(benzylidene amino) -2-thioxo-6-methyl 2,5-dihydropyrimidine-4(3H)-one (LS])and 3-(benzylidene amino)-6-methyl pyrimidine 4(3H, 5H)-dione(LA)as chelating ligands), were used to prepare some complexes of Cr(III), La(III), and Ce(III)] ions. Standard physico-chemical procedures including metal analysis M%, element microanalysis (C.H.N.S) , magnetic susceptibility, conductometric measurements, FT-IR and UV-visible Spectra were used to identify Metal (III) complexes and Schiff bases (LS) and (LA). According to findings, a [Cr(III) complex] showed six coordinated octahedral geometry, while [La(III), and Ce(III) complexes]were structured with coordination number seven. Schiff's bases a
... Show MoreIn present work, new tetra-dentate ligand, titled 3,5-bis ((E)-5-Bromo-2-hydroxy benzylidene amino) benzoic acid (H3L), was prepared via an acid-catalyzed condensation process. New four metallic ligand complexes with Co(II), Ni(II), Cu(II) and Zn(II) ions, were also prepared from the refluxing of equivalent moles. Ligand's structure and its complexes; were confirmed by numerous characterization methods, including Ultraviolet-Visible, Infrared, Mass Spectrometer, 1H and 13C Nuclear Magnetic Resonance spectra, atomic absorption, magnetic moments, and molar conductivity measurements. The results of the spectroscopic analyzes proved that the prepared ligand acts as tetradentate bi-ionic ligand and it was bond
... Show MoreFunctional strength is one of the most important elements of physical preparation and an important physical characteristic in our daily life in general and sports training in particular, as it is the most influential characteristic in all sporting events, which the athlete must possess in order to reach the highest levels and achieve the best results. The research aimed to prepare functional strength training exercises According to the gradual increase in load in the development of some physical abilities and achievement for men's 100 meter competition runners , And to identify the effect of functional strength training according to the gradual increase in load in developing some physical abilities and achievement for men’s 100-
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