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.
Optical properties and surface morphology of pure and doped Polystyrene films with different divalent metals of Zn, Cu and Sn and one concentration percentage have been studied. Measurements of UV-Vis spectrophotometer and AFM spectroscopy were determined. The absorbance, transmittance and reflectance spectrums were used to study different optical parameters such as absorption coefficient, refractive index, extinction coefficient and energy gap in the wavelengths rang 200-800nm. These parameters have increased in the presence of the metals. The change in the calculated values of energy gaps with doping metals content has been investigated in terms of PS matrix structural modification. The value of opt
... Show MoreThis contribution reports a comprehensive investigation into the structural, electronic and thermal properties of bulk and surface terbium dioxide (TbO2); a material that enjoys wide spectra of catalytic and optical applications. Our calculated lattice dimension of 5.36 Å agrees well with the corresponding experimental value at 5.22 Å. Density of states configuration of the bulk structure exhibits a semiconducting nature. Thermo-mechanical properties of bulk TbO2 were obtained based on the quasi-harmonic approximation formalism. Heat capacities, thermal expansions and bulk modulus of the bulk TbO2 were obtained under a wide range of temperatures and pressures. The dependency of these properties on operational pressure is very evident. Cle
... Show MoreThe concept of forming the living space in the American strategic thought has an
important position it is regarded as an strategic movement that it supports the American
United States with the huge capabilities in its own concern that enables it to approach of
American administration , we find that of different historical periods it works to establish that
the geopolitical dimension which is accompanied with the ability of American response for
the evens that in its own turn enables the American united states to seize the growing chances
in the global strategic environment This study includes five chapters :
- Chapter one: The idea of living space.
- Chapter two: Geopolitical dimension of living space theory.
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Background: Currently there are four general approaches to correct refractive errors: refractive corneal surgery, crystalline lens surgery and implantation of an intraocular lens in anterior or posterior chamber. Aim: To evaluate the predictability, safety and stability of toric phakic implantable collamer lens implantation to correct moderate to high myopic astigmatism. Methods: Sixty eyes of 40 patients underwent implantation of a toric implantable collamer lens (V4c design) in the Eye Specialty Private Hospital, Baghdad, Iraq were studied. The mean spherical refraction was -11.32±3.17 diopter (D) with a range of -6.00 to -18.00 D and a mean cylinder of -2.61±1.16 with range of -1.00 to -5.50 D. The outcome measures that evaluat
... Show MoreMulti-drug-resistant uropathogenic Escherichia coli (UPEC) is considered a significant challenge due to its ability to resist antibiotics and form biofilms. UPEC biofilm formers are well protected and largely inaccessible to antibiotics, which leads to persistent infections and evasion of the host immune system. Understanding how ciprofloxacin and trimethoprim/sulfamethoxazole affect biofilm formation is essential for improving treatment strategies for urinary tract infections (UTIs). A total of 76 UPEC isolates were obtained from Iraqi patients and identified using morphological and biochemical characteristics, as well as the Vitek®-2 Compact system. Minimum inhibitory concentrations (MICs) were determined using the Vitek®-2 system, whic
... Show MoreThis study unveils the ideologies of women empowerment encoded in the Mona Lisa Smile movie (2003). It reveals how the stereotypical image of women born only to be wives and do the duties of upbringing and housework is challenged. Katherine Ann Watson (Julia Roberts), the main character in the movie, wants to make a difference in the next generation of women. She rejects the imposed traditional ideologies. Linguistically, she opposes conventional thinking and seeks to persuade her students that life is about more than getting married. The primary focus of this study is to examine and clarify how the characters’ linguistic choices convey their ideologies concerning the notion of women empowerment. To do this, the researchers apply
... Show MoreBackground: Complete removal of filling material from the root canal is an essential requirement for endodontic retreatment. The purpose of the present study is to evaluate and compare the dissolving capabilities of various solvents (Xylene, Eugenate Desobturator, Eucalyptol, EDTA and Distilled water (as a control)) on four different types of sealer (Endofill, Apexit Plus, AH Plus and EndoSequence bioceramic sealer). Materials and method: Eighty samples of each sealer were prepared according to the manufacturers' instructions and then divided into ten groups (of 8 samples) for immersion in the respective solvents for 2 and 5 min immersion periods. Each sealer specimen was weighed to obtain its initial mass. The specimens were immersed in
... Show More2- amino -5- thiol-1,3,4- thiadiazole (S1) was prepared by cyclic locking of thiosemicarbazide in the presence of anhydrous sodium carbonate and CS2. diazotization of (S1) compound gave diazonium salt (S2) that reacts with different activated aromatic compounds to get the following azo compounds ,2 [(4- aminophenyl) diazenyl ] 1,3,4- thiazdiazole-5- thiol (S3) ,2-[4-amino- 1-naphthyl diazenyl] -1,3,4 – thiazdiazole-5-thiol (S4) , 3-amino-4-[(5- mercapto -1,3,4- thiadiazole -2-yl) diazenyl ] phenol(S5) ,1-[(5-mercapto-1,3,4-thiadiazole-2-yl) diazenyl] -2-naphthol (S6) , 5-{[4-(dimethylamino) phenyl] diazenyl}-1,3,4-thiadiazole-2- thiol(S7) ,5-{[4-(diethylamino) phenyl] diazenyl}-1,3,4- thiadiazole-2- thiol(S8) ,2- amino-5-[(5-mercapto-1,3
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