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.
In this study, the aqueous extract of (Typha domingensis Pers.) pollen grain (qurraid) to know its ability to manufacture silver nanoparticles. Qurraid is a semi-solid yellow food substance, sold in Basra markets and eaten by the local population. It is made from the pollen of the T. domingensis Pers. plant after being pressed and treated with water vapor. The Gas chromatography–mass spectrometry (GC-MS) reaction was done to identify the active compounds of qurraid aqueous extract. The ability of the aqueous extract of qurraid to manufacture silver nanoparticles was tested, and the construction of silver nanoparticles was inferred by the reaction mixture's color, which ranged from yellow to dark brown. The synthesi
... Show MoreBackground: White spot lesion is the first visible sign of dental caries that is characterized by demineralized lesion underneath an intact surface. Several studies demonstrated that they could be treated using noninvasive techniques like the use of fluoride or casein phospho-peptide and amorphous calcium phosphate. Improvement in aesthetic outcomes by covering the demineralized enamel is one of the advantages of the use of resin infiltration and opal-ustre microabrasion, which are two new techniques that had been used for treatment of white spot lesion. The purpose of this study was to evaluate the impact of resin infiltration and microabrasion in the microhardness of the artificial white spot lesions at various depths. Material and method
... Show MoreComposite steel-concrete sections have a broad benefit through increasing structural strength as well as minimizing the self-loads. All past researches were concerned with pre-installed shear connectors (PRSC) in the manufacturing of composite sections. A new fabrication technique for steel-concrete-steel composite sections were presented in the current study by the post-installation shear connectors (POSC) passed-through an embedded polymerizing vinyl chloride (PVC) pipes. The performance of normal strength concrete prisms with a specified strength of 32 MPa connected to square steel tubes (SST) was investigated. Six specimens were fabricated in both methodologies, PRSC and POSC were experimentally tested by Push-out test. The spac
... Show MoreThe present work represents a theoretical study for the correction of spherical aberration of an immersion lens of axial symmetry operating under the effect of space charge, represented by a second order function and preassigned magnification conditions in a focusing of high current ion beams. The space charge depends strongly on the value of the ionic beam current which is found to be very effective and represents an important factor effecting the value of spherical aberration .The distribution of the space charge was measured from knowing it's density .It is effect on the trajectory of the ion beam was studied. To obtain the trajectories of the charged particles which satisfy the preassined potential the axial electrostatic potential w
... Show MoreThis study aimed to determine the effect of varicocelectomy on sperm parameters, oxidant- antioxidant status and chromatin maturity percent. The current study has been conducted on 154 infertile patients complaining from varicocele and varicocelomized men in addition to 25 fertile men as control. The results revealed significant decrease (P<0.05) in sperm concentration, progressive motile sperm percent, normal sperm morphology percent, GSH, SOD1, CAT levels and chromatin maturity percent and significant increase (P<0.05) in MDA and ROS concentrations in infertile patients with varicocele when compared to fertile men. The results revealed improvement (P<0.05) of sperm parameters quality, GSH, SOD1, CAT, MDA, ROS concentration and chromatin m
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