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.
A series of metal ion complexes of some divalent transition metal ions having the general composition [ML2Cl2]nH2O with 2-(benzo[d]thiazol-2-ylamino)-2- (5-chloro-2-hydroxy phenyl) acetonitrile ligand has been prepared from 5-chloro-2-hydroxy-benzaldehyde and benzo[d]thiazol-2-amine. Existence of cyanide as potassium cyanide in acidic medium was considered, characterized by elemental chemical analysis, conductance of molarity, magnetic susceptibility measurements, FTIR electronic spectral studies and mole ratio method. FTIR indicates the participation of amino and acetonitrile nitrogen which is coordinated with the central metal ion.
The present paper is devoted to studying the imitation of some Quran phrases and words in the tale of "The Leprous Girl". The paper aims at identifying the common ground between the tale and some great stories related in the verses of the holy Quran, and comparing the original work with the present translation. First, we translated the tale from Russian into Arabic so as to be tackled in study, and then an identification of the commonalities between this tale and the Quran wording is made. It was found that texting is clear in the original text of the tale, hence the need for this paper. By studying the texts and phrases employed by the writer, we observe that the text is influenced by the Quranic stories whose effects have been reflecte
... Show MoreA novel ligand, (E)-5-((2-hydroxy-4,6-dimethylphenyl)diazenyl)-2,3-dihydrophthalazine-1,4- dione, was synthesized through the reaction of 3,5-dimethylphenol with the diazonium salt of 5-amino-2,3-dihydrophthalazine-1,4-dione. The ligand underwent characterization through the utilization of diverse spectroscopic methods, including UV-Vis, FT-IR, 13C, and 1H-NMR, alongside Mass spectroscopy and micro elemental analysis (Carbon, Hydrogen, Nitrogen, and Oxygen). Metal chelates of transition metals were prepared and analyzed using elemental analysis, mass spectra, atomic absorption, UV-Vis, FT-IR spectral analysis, as well as conductivity and magnetic measurements. The investigation into the compounds’ nature was conducted by utilizing mole r
... Show MoreThe research aims to identify the positives formulation entrances authors depending on the setting retaining the names of the authors of Arab veterans and cons of setting the entrances to Arab authors ancient depending on the nickname by desktop diligence without reference to a setting retaining the potential to benefit other libraries disciple of retaining existing in sober university libraries. Use the survey method and adopted a questionnaire distributed to the research sample consisting of employees working in the libraries in question and the total number of forms that have been distributed (50) form .tousel search phrase conclusions from them .
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... Show MoreAnaemia is a common extra-articular manifestation of rheumatoid arthritis (RA) where anaemia of chronic disease (ACD) and iron deficiency anaemia (IDA) are the two most frequent types. The distinction between these two types of anaemia has always been challenging requiring sophisticated techniques. Serum transferrin receptor (sTfR) a truncated soluble form of the transferrin receptor is one of the parameters that is influenced by the Iron content and supply to the erythrons and is not affected by inflammatory status and therefore the use of the sTfR/log ferritin (sTfR-F) index can be a reliable indicator of functional iron deficiency.
Purpose: This study aimed to compare the stability and marginal bone loss of implants inserted with flapped and flapless approaches 8 weeks after surgery and 3 months after loading. Material and Methods: Thirty SLActive implants were inserted in 11 patients and early loaded with final restoration 8 weeks after healing period. The stability values determined by Osstell and the marginal bone loss measured by CBCT at the initial time (1st) and 8 weeks of the healing period (2nd) and 3 months after loading (3rd). Results: The overall survival rate was 100%. A significant increase in the 3rd implant stability value in the age of ˂ 40. A significant decrease in the 2nd implant stability value in both gender and traumatic zone with a flapless app
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