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.
Background: The use of the cone beam computed tomography for analysing the position of the greater palatine foramen in relation to various anatomical landmarks is crucial in dentistry. The aims of the current study, firstly is to determine the greater palatine foramen position in relation to various anatomical landmarks by using cone beam computed tomography and secondly is to make a comparison of the measurements according to side, gender, and age. Materials and methods: This prospective study included 60 Iraqi patients (28males and 32 females) who selected according to availability of Inclusion criteria, which include age range (21 - 60 years), with no dentofacial deformities or pathological lesion at the maxilla. All patients had inform
... Show Moreγ-Al2O3–NPs were synthesized by a green synthesis process based on Boswellia carterii resin extract and aluminum sulphate in an alkaline medium. Boswellia carterii resin extract is a significant reducing and stabilizing agent for synthesizing γ-Al2O3–NPs.Several techniques, including Fourier–transform infrared (FT-IR), UV–visible spectroscopy, x-ray diffraction, electron microscopy (XRD), energy dispersive x-ray (EDX), scanning electron microscopy (SEM), Transmission electron microscopy (TEM), and atomic force microscopy (AFM), were utilized to investigate the final product. XRD and SEM confirmed a plate-like crystalline structure with an average size of 17.5 nm. FT-IR analysis identified aluminum oxide stretching vibrations (655,
... Show MoreWe have synthesized many metal (II) complexes using curcumin L1 as the major ligand and 2-(1H-Benzimidazol-2-yl) aniline L2 as a supporting ligand. The complexes were characterized by spectroscopy methods such as; molar conductivity, elements microanalysis, Fourier-transform spectroscopy (FT-IR), UV-vis, and mass spectroscopy. Both curcumin ligands and L2 were found to be capable of binding to M(II) and metal ions via their two N atoms, according to the data. The formula for the complexes is the same. [M (L1)(L2)H2OCl], where M is Ni(II), Co(II), Cu(II), Cd(II), and Hg(II) (II). Octahedral complexes are proposed for the prepared compounds. The bio-actives suggested that the complexes are effective against bacteria and fungus on a mi
... Show MoreInflammatory bowel disease (IBD) is a common chronic inflammatory disease of the gastrointestinal tract, including ulcerative colitis and Crohn's disease. ulcerative colitis (UC) disease is characterized by chronic, persistent, recurrent, and nonspecific intestinal ulcers and mucosal inflammation. This study investigated the protective effects of cinnamic acid on dextran sodium sulfate (DSS) induced ulcerative colitis in mice. Forty adult male mice were collected and randomly divided into five groups, group Ӏ received a suspension of distill water and poloxamer, and group ӀӀ received 3% DSS in drinking water for 7 consecutive days. Two treatment groups received an oral suspension of cinnamic acid 50 and 25 mg/kg respectively an
... Show MoreAceclofenac (AC) is an orally active phenyl acetic acid derivative, non-steroidal anti-inflammatory drug with exceptional anti-inflammatory, analgesic and antipyretic properties. It has low aqueous solubility, leading to slow dissolution, low permeability and inadequate bioavailability. The aim of the current study was to prepare and characterize AC-NS-based gel to enhance the dissolution rate and then percutaneous permeability. NS.s were prepared using solvent/antisovent precipitation method at different drug to polymer ratios (1:1, 1:2, and 1:3) using different polymers such as poly vinyl pyrrolidone (PVP-K25), hydroxy propyl methyl cellulose (HPMC-E5) and poloxamer® (388) as stabilizer
... Show MoreContracting cancer typically induces a state of terror among the individuals who are affected. Exploring how chemotherapy and anxiety work together to affect the speed at which cancer cells multiply and the immune system’s response model is necessary to come up with ways to stop the spread of cancer. This paper proposes a mathematical model to investigate the impact of psychological scare and chemotherapy on the interaction of cancer and immunity. The proposed model is accurately described. The focus of the model’s dynamic analysis is to identify the potential equilibrium locations. According to the analysis, it is possible to establish three equilibrium positions. The stability analysis reveals that all equilibrium points consi
... Show MoreThe idea of ech fuzzy soft bi-closure space ( bicsp) is a new one, and its basic features are defined and studied in [1]. In this paper, separation axioms, namely pairwise, , pairwise semi-(respectively, pairwise pseudo and pairwise Uryshon) - fs bicsp's are introduced and studied in both ech fuzzy soft bi-closure space and their induced fuzzy soft bitopological spaces. It is shown that hereditary property is satisfied for , with respect to ech fuzzy soft bi-closure space but for other mentioned types of separations axioms, hereditary property satisfies for closed subspaces of ech fuzzy soft bi-closure space.
In this paper we estimate the coefficients and scale parameter in linear regression model depending on the residuals are of type 1 of extreme value distribution for the largest values . This can be regard as an improvement for the studies with the smallest values . We study two estimation methods ( OLS & MLE ) where we resort to Newton – Raphson (NR) and Fisher Scoring methods to get MLE estimate because the difficulty of using the usual approach with MLE . The relative efficiency criterion is considered beside to the statistical inference procedures for the extreme value regression model of type 1 for largest values . Confidence interval , hypothesis testing for both scale parameter and regression coefficients
... Show MoreObjective: Develop a deliberate thinking scale for the setting skill in volleyball for second-year female students in the College of Physical Education and Sports Sciences for Woman. Research methodology: The researchers used the experimental approach, employing a two-group approach (pre-test and post-test), to suit the nature of the research. The research community comprised (65) second-year female students from the College of Physical Education and Sports Sciences for Woman at the University of Baghdad for the academic year 2024-2025. The research sample was randomly selected, with (15) students in Section A, the experimental group, and (15) students in Section B, the control group. This group represented (46%) of the students. Th
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