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.
The author’s research is dedicated to the actual problem of identifying the linguoculturological and translation features of the glutonic vocabulary both in Russian and in Arabic. It is noted that the vocabulary of the glutonic type is extremely rich and diverse, as it is part of the national and linguistic culture of the Russian and Arab people. In the gastronomic discourse of the Russian people and the Arab peoples, it is represented by various parts of speech. The study of the traditions of food consumption confirmed the rich stylistic possibilities of the glutonic vocabulary, the names of bread in Russian and Arabic languages. It has been established that in modern Russian gastronomic discourse, glutonic lexical units are involved
... Show MoreBackground: The new concepts and technologies continue to change the dynamics of endodontic practices in the world. Rapid and significant changes in techniques, instrument design, and the type of metals used to manufacture endodontic instruments which have been made during the last few years in an attempt to overcome canal preparation errors. The purpose of this study is to measure and compare canal transportation and centering ability of Self Adjusting File with two rotary nickel-titanium (Ni-Ti) systems, ProTaper and BioRaCe at different levels. Material and Methods: Forty five distal roots of mandibular first molars with moderate curvature were selected using Schneider method. Roots were divided randomly into 3 groups of 15 each and were
... Show MoreThe study was conducted over the period of Oct 2018 to Apr 2019 and is aimed for the detection and estimation of four hazardous Volatile Organic Compounds VOC (benzene, toluene, ethylbenzene, and xylene) so-called (BTEX) in samples collected from the produced water in the Al-Ahdab oil field in Iraq also to track their availability in the important natural water sources around the field. These compounds pose a risk to human health as well as environment. To avoid the laborious and tiresome conventional extraction methods, water samples were collected and concentrated using solid-phase extraction technique (SPE) which is a robust and cost-effective method of sample extraction with minimal exposure and handling of solvents and then to be analy
... Show MoreAllosteric inhibition of EGFR tyrosine kinase (TK) is currently among the most attractive approaches for designing and developing anti-cancer drugs to avoid chemoresistance exhibited by clinically approved ATP-competitive inhibitors. The current work aimed to synthesize new biphenyl-containing derivatives that were predicted to act as EGFR TK allosteric site inhibitors based on molecular docking studies.
A new series of 4'-hydroxybiphenyl-4-carboxylic acid derivatives, including hydrazine-1-carbothioamide (S3-S6) and 1,2,4-triazole (S7-S10) derivatives, were synthesized and characterized using IR, 1HNMR, 13CNMR
Abstract Physical requirements are an important priority for the development of football gymnastics coaches because the nature of performance is interconnected and interconnected in terms of the player's duties in the match. In the gameplay situations, the player must perform the skill with strength and speed coupled with accuracy and the reactions of the colleague and competitor alike, which represents the normal reality of the football gymnasium Skilled exercises are one of the most suitable technical side exercises as they are built according to the components of the skill requirements of the game and the nature of its performance, which appear on the gro
... Show MoreThe studies on unbonded post-tensioned concrete members strengthened with Carbon Fiber Reinforced Polymers (CFRPs) are limited and the effect of strengthening on the strain of unbonded pre-stressed steel is not well characterized. Estimating the flexural capacity of unbound post-tensioned members using the design methodology specified in the design guidelines for FRP strengthening techniques of bonded post-tensioned members does not provide a reliable evaluation. This study investigates the behavior of unbonded post-tensioned concrete members with partial strand damage (14.3% and 28.6% damage) and strengthened with CFRP laminates using a near-surface mounted technique with and without U-wrap anchorages. The experimental results show
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