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.
Conclusion and results
1. The research concluded through considering the rhetorical visions,
appropriate relationships between utterances with a language derived
from the reality of the social, religious, and, cultural life.
2. The poet compound between realism and the documentation of the
poetic structure, its depth, and the conjugation of its symbolic
metaphors, and also between its phonetic music and the right artistic
nature and the inanimate rules to take in consideration what Dr. Ahmad
Haikal concluded that the tried to com up with something better than
that of the previous generation, but he is still following their orbit, and
their trend method of poem building.
3. The realistic images visionary r
Fadak farm project was selected to conduct this study in and to evaluate the state of quality and health indices in term of soil physical properties, where this farm is located in Holly Najaf Governorate. Some physical properties (soil texture, mean weight diameter, bulk density, porosity, infiltration rate, saturated hydraulic conductivity and available water) were selected to assess the quality then health indices, Results showed that classes of moderate and poor soil health were dominated in lands of this farm for physical properties It was noted that the class good of soil health wasnot collaterally appeared in areas for the physical characteristics.
The pharmacokinetics and bioequivalence of a newly developed extended-released (ER) tablet containing 400 mg pentoxifylline as a test product was compared with the reference brand product Trental® 400 mg ER tablet produced by Sanofi-Aventis. Two separate studies were conducted simultaneously. The first study was conducted under fasting condition, whereas, the second study was conducted under fed condition; using the same batches of the test and reference products in both studies. In each study, both products were administered to 32 healthy male adult volunteers applying a single-dose, two-treatment, two-period, two-sequence, randomized crossover design with one-week washout period between dosing. Twenty two blood samples we
... Show MoreDiarrhea is one of the most commonly encountered minor ailments in the community pharmacies. It is associated with significant morbidity and mortality. However, the majority of pharmacists in Iraq did not manage diarrheal cases in a proper way. Therefore, the current study aimed to evaluate the benefit of a new mobile application (diarrhea management step by step) to improve the pharmacist's role in the management of diarrhea. The study was conducted from 21th September to 21th October 2021 using a pre-post design via a simulated patient (SP) technique. A validated diarrhea scenario was presented to each pharmacist by the SP twice, once before and the other after giving the mobile application to the pharmacist. Furthermore, pharmaci
... Show MoreBackground: An accurate adaptation of the crown to the finish line is essential to minimize cement dissolution and to preserve periodontium in fixed partial denture cases. An accurate adaptation of crown is possible only when preparation details are captured adequately in the impression and transferred to cast. For these reasons, gingival displacement is necessary to capture subgingival preparation details.The aim of the present study is to measure in vivo the horizontal displacement of the gingival sulcus obtained by using three new cordless retraction materials (Magic Foam Cord®, Racegel and Astringent Retraction Paste) in comparison to medicated retraction cord. Materials and method: Thirty-two patients requiring porcelain fused to me
... Show MoreThe current research aimed to conducting two experiments to study the effect of coating hatching eggs with nano-titanium dioxide (nano-TiO2) and nano-silica dioxide (nano-SiO2) particles and their mixture with carboxymethyl cellulose (CMC) on the characteristics of hatching percentage, embryo growth inside the egg. The study was conducted in the Department of Animal Production, College of Agriculture, Tikrit University for the period from 19/3/2023 to 17/9/2024. It aimed to evaluate the coating of hatching eggs with Nano-TiO2 and Nano-SiO2 particles and their mixture with carboxymethyl cellulose CMC on the qualities of hatching percentage, embryo growth inside the egg, as well as trying to obtain the best and longest storage method for fert
... Show MoreThis study investigates the stomach morphology and histochemistry of Clarias gariepinus. Grossly, the stomach is a J-shaped organ with three distinct regions: cardiac, fundic, and pyloric. Histologically, its wall comprises four layers: mucosa, submucosa, muscularis externa, and serosa. The mucosa exhibits broad longitudinal folds lined by high columnar cells with basal oval nuclei. These cells contain apical mucosubstances that react positively with Periodic Acid Schiff (PAS) stain and negatively with Alcian Blue (AB). Gastric pits result from mucosal invaginations. Glands are present in the fundic and cardiac regions but absent in the pyloric. Oxynticopeptic cells exclusively line the fundic glands. Enteroendocrine cells are distr
... Show MoreThis study investigates the stomach morphology and histochemistry of Clarias gariepinus. Grossly, the stomach is a J-shaped organ with three distinct regions: cardiac, fundic, and pyloric. Histologically, its wall comprises four layers: mucosa, submucosa, muscularis externa, and serosa. The mucosa exhibits broad longitudinal folds lined by high columnar cells with basal oval nuclei. These cells contain apical mucosubstances that react positively with Periodic Acid Schiff (PAS) stain and negatively with Alcian Blue (AB). Gastric pits result from mucosal invaginations. Glands are present in the fundic and cardiac regions but absent in the pyloric. Oxynticopeptic cells exclusively line the fundic glands. Enteroendocrine cells are distr
... Show More