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 spreading of the pandemic coronavirus disease (COVID-19) is formulated mathematically. The objective of this study is to stop or slow the spread of COVID-19. In fact, to stop the spread of COVID-19, the vaccine of the disease is needed. However, in the absence of the vaccine, people must have to obey curfew and social distancing and follow the media alert coverage rule. In order to maintain these alternative factors, we must obey the modeling rule. Therefore, the impact of curfew, media alert coverage, and social distance between the individuals on the outbreak of disease is considered. Five ordinary differential equations of the first-order are used to represent the model. The solution properties of the system ar
... Show MoreIn recent years, the Global Navigation Satellite Services (GNSS) technology has been frequently employed for monitoring the Earth crust deformation and movement. Such applications necessitate high positional accuracy that can be achieved through processing GPS/GNSS data with scientific software such as BERENSE, GAMIT, and GIPSY-OSIS. Nevertheless, these scientific softwares are sophisticated and have not been published as free open source software. Therefore, this study has been conducted to evaluate an alternative solution, GNSS online processing services, which may obtain this privilege freely. In this study, eight years of GNSS raw data for TEHN station, which located in Iran, have been downloaded from UNAVCO website
... Show MoreA numerical computation for determination transmission coefficient and resonant tunneling energies of multibarriers heterostructure has been investigated. Also, we have considered GaN/Al0.3Ga0.7N superlattice system to estimate the probability of resonance at specific energy values, which are less than the potential barrier height. The transmission coefficient is determined by using the transfer matrix method and accordingly the resonant energies are obtained from the T(E) relation. The effects of both well width and number of barriers (N) are observed and discussed. The numbers of resonant tunneling peaks are generally increasing and they become sharper with the increasing of N. The resonant tunneling levels are sh
... Show MoreThe research aims to answer the questions that revolve in the mind of mankind about how to create creation, how it existed prior to creation, who created existence, and the characteristics of that presence. The researcher also wanted to show that the culture of Imam Ali (peace be upon him) In the book of Adam, peace be upon him, God has punished Adam (peace be upon him) for not having sinned. Because his wife is the one who fed him the fruit of the tree, and this is contrary to what was stated in the sermon of Imam (peace be upon him) who Z Adam (peace be upon him) is the one who trusted Satan and Gwighth.
We note that the approach of the rhetoric has pointed to the creation of angels and did not refer to
... Show MoreThe study aims to select suitable ornamental plant species that can survive relatively with high concentrations of acetaminophen and methylparaben in constructed wetlands. Alternanthera spp, Asparagus aethiopicus and Chlorophytum comosum are examined to withstand three initial concentrations, 20, 100 and 200 mg/L of acetaminophen and methylparaben. A total of 21 plastic pails with each 3 L capacity consisting of nine pails are used for each pharmaceutical and personal care products (PPCPs) compounds (acetaminophen and methylparaben) for three ornamental plants (Alternanthera spp, Asparagus aethiopicus and Chlorophytum comosum), with three pails as plant controls. The results reveales
... Show MoreBackground: This study aimed to compare the surface microhardness (MH) and mineral content of white spot lesions(WSLs) after using bioactive glass (BAG)casein phosphopep-tides-amorphous calcium phosphate(CPP-ACP),and nanohydroxyapatite(Nano-HAP) under pHcycling. Material and method:18 sound maxillary first premolar were used for the study.10 were selected for the vickers microhardness test, For Energy-dispersive X-ray spectroscopy analysis (EDX), the remaining 8 premolar teeth were used, 40 sections of enamel blocks (Four from each tooth) were produced from the middle part of the buccal and palatal surfaces of teeth for MH test while 48 sections of enamel blocks (Six from each tooth) were produced for EDX analysis. Enamel slabs were
... Show MoreBackground: Antibacterial action of root canal filling is an important factor for successful root canal treatment, so the aim of the study was to identify and to compare the antimicrobial effect of new sealer (GuttaFlow) to commonly used endodontic sealers (AH Plus, Apexit and EndoFill) against four endodontic microbes. Materials and methods: Twenty patients aged (30-40) years with infected root canals were selected. Four types of microorganisms were isolated from root canals (E faecalis, Staphylococcus aureus, E coli and Candida albicans) and cultured on Mueller Hinton agar Petri-dishes. After identification and isolation of bacterial species, agar diffusion method was used to assess the antibacterial action of four contemporary endodontic
... Show MoreObjective: To determine the correlation between the second derivative of digital pulse wave and the QT variability index. Method: The cross-sectional study was conducted from October 2021 to May 2022 at the Department of Physiology, College of Medicine, University of Mustansiriyah, Baghdad, Iraq, and comprised healthy women. Samples were raised by simple random technique. Digital pulse waves were captured using a fingertip pulse wave transducer. Lab Chart Pro version 7.2 was used to automatically detect and quantify the amplitude of A, B, C, D and E waves expressed by the second derivative. QT interval of each beat was recorded by electrocardiogram, and was calculated automatically via Lab chart Pro version 7.2 without averaging. D
... Show MoreIn the present work, a set of indoor Radon concentration measurements was carried out in a number of rooms and buildings of Science College in the University of Mustansiriyah for the first time in Iraq using RAD-7 detector which is an active method for short time measuring compared with the passive method in solid state nuclear track detectors (SSNTD's). The results show that, the Radon concentrations values vary from 9.85±1.7 Bq.m-3 to 94.21±34.7 Bq.m-3 with an average value 53.64±26 Bq.m-3 which is lower than the recommended action level 200-300 Bq/m3 [ICRP, 2009].
The values of the annual effective dose (A.E.D) vary from 0.25 mSv/y to 2.38 mSv/y, with an average value 1.46±0.67 mSv/y which is lower than the recommended the rang