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.
Corruption, in all its categories and forms, is regarded as the nowadays virus which has greatly spread in most institutes and society, a matter that cause a great waste of resources.
According to the reports of international transparency Institute, Iraq is regarded as one of the greatest countries in corruption.
Regardless of the reasons and forms of corruption, the retreat in work – values and ethics are the main reasons behind that.
Being the main source of providing qualified staff "educators" for the working market, the high education institutes face great challenges in standing against corruption inside and outside
... Show MoreIn this paper, split-plate airlift electrochemical reactor as an apparatus with new configuration for wastewater treatment was provided. Two aluminum plates were fixed inside the reactor and present two functions; first it works as split plates for internal loop generation of the airlift system (the zone between the two plates acts as riser while the other two zones act as downcomer) and second it works as two electrodes for electrocoagulation process. Simulated wastewater contaminated with zinc ions was used to test the performance of this apparatus for zinc removal by studying the effect of different experimental variables such as initial concentration of zinc (50-800 ppm), electrical current density (2.67-21.4 mA/cm2), init
... Show MoreIn this work, the relationship between the ionospheric parameters (Maximum Usable Frequency (MUF), Lowest Usable Frequency (LUF) and Optimum working Frequency (OWF)) has been studied for the ionosphere layer over the Iraqi zone. The capital Baghdad (44.42oE, 33.32oN) has been selected to represent the transmitter station and many other cities that spread over Iraqi region have represented as receiver stations. The REC533 communication model considered as one of the modern radio broadcasting version of ITU has been used to calculate the LUF parameter, while the MUF and OWF ionospheric parameters have been generated using ASAPS international communication model which represents one of the most advanced and
... Show MoreThe study aims to determine the concentrations of radon, humidity, and CO2 in residences within the Mitham Al-Tammar neighbourhood of Kufa, utilising an Airthings 2960 Wave Plus device in the living rooms of each household. The concentration of radon varied, with a minimum value of 13 ± 3.9 Bq/m3 and a maximum value of 90 ± 5.8 Bq/m3, yielding an average rate of 35.8 ± 4.889 Bq/m3. The concentrations of total VOCs in residences ranged from 69.26 ppb to 810.14 ppb, with a mean of 321.4855 ± 40.4. The humidity percentages exhibited a minimum concentration of 51.68% and a maximum of 122.97%, averaging 76.594 ± 4.298. The concentrations of volatile organic compounds and
... Show MoreBack ground: Skin grafting is the most common form
of reconstructive surgery, and regeneration of
sensations in skin grafts is a complex process
influenced by many factors such as , the thickness of
the graft, the depth of the grafted bed, meshing of the
graft, the condition of the bed and the surrounding
area. So many studies performed on this subject, some
of them clinically based on subjective type of sensation
tests, and others histological to detect the presence of
nerve fibers in the grafted skin
Objectives: To detect return of sensations to split
thickness skin grafts by clinical methods.
Methods: From Oct. 1995 to Oct. 2010, a clinical
prospective study performed in Al wasity Hospital for
Topology and its applications occupy the interest of many researching centers in the advanced world. From this point of view and because the near open sets play a very important role in general topology and they are now the research topics of many topologists worldwide and its sets doesn’t enter in fibrewise topology yet. Therefore, we use some of the near open sets to be model for introduce results and new spaces in fibrewise topological spaces. Also, there is a very important role of closure operators in constructing a topological spaces, so we introduce a new closure operators on the power set of vertices on graphs and conclusion theorems and new spaces from it. Furthermore, we discuss the relationships of connectedness between some ty
... Show MoreThis paper is concerned with introducing and studying the o-space by using out degree system (resp. i-space by using in degree system) which are the core concept in this paper. In addition, the m-lower approximations, the m-upper approximations and ospace and i-space. Furthermore, we introduce near supraopen (near supraclosed) d. g.'s. Finally, the supra-lower approximation, supraupper approximation, supra-accuracy are defined and some of its properties are investigated.
The main objective of the central bank is to achieve price stability and target in fractionates. Therefore, the bank sought to use modern tools and policies in order to reduce the negative effects of the accumulation of foreign reserves represented by monetary sterilization, similar to developed and developing countries alike, but with different available tools that are possible and imposed by the local financial and monetary environments, such as the window for buying and selling foreign currency, open market operations and deposit facilities. And lending existing. Because any in crease in the monetary base resulting from the accumulation of foreign reserves will affect price stability directly due to the consumer nature of the
... Show MoreThe God Almighty prefer on the Arab nation, and entrusted to carry his message to the secular world as a whole, , gave her all necessities of life in terms of location, who are the heart in the earth's surface. From this blessed place emerged the greatest civilizations and the world has ever known for it than in human history, a four empires Alsamyat