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.
Drug misuse is defined as using of drugs for a non-therapeutic or non-medical purpose. In Iraq drug misuse is a major problem because almost any drug can be easily obtained from pharmacies. Appetite- stimulant drugs are example of drugs that are widely used without a prescription. The study included 230 patients who use these drugs in Babylon. A questionnaire included the following questions ; age, sex, marital state, the reason for use the drug , whether the drug is prescribed by physician or not , type of drug used , the frequency of daily dose and lastly the extent of side effects of the drugs used. The results showed that the age range of 35% of subjects were (17-21) years old and 70% of participants were females. The study also show
... Show MorePhenol oxidation by Fenton's reagent (H2O2 + Fe+2) in aqueous solution has been studied for the purpose of learning
more about the reactions involved and the extent of the oxidation process, under various operating conditions. An initial
phenol concentration of 100 mg/L was used as representative of a phenolic industrial wastewater. Working temperature
of 25C was tested, and initial pH was set at 5.6 . The H2O2 and the Fe+2 doses were varied in the range of
(H2O2/Fe+2/phenol = 3/0.25/1 to 5/0.5/1). Keeping the stirring speed of 200 rpm.
The results exhibit that the highest phenol conversion (100%) was obtained under (H2O/Fe+2/phenol ratio of 5/0.5/1)
at about 180 min. The study has indicated that Fenton's oxidation i
Provisions of combat games In Islamic Jurisprudence
The training of great importance in the play, in building optic and intellectual broadcast codes tags, and then comes after the recipient at the reception of such codes and decoded tags, and is the rhythm, the color of the most important elements of configuration, consistent with other elements, Kaltmathl, and focus, and harmony, and dissonance
Physical adsorption by nitrogen gas was studied on seven commercial platinum reforming catalysts (RG-402, RG-412, RG-432, RG-451, RG 422,RG-482, PS-10), four prepared platinum catalysts (0.1%Pt/alumina, 0.2 %Pt/alumina, 0.45 %Pt/alumina and 0.55% Pt/alumina), and -alumina support. Physical adsorption was carried out by using Accelerated Surface Area and Porosimetry (ASAP 2400 device) at 77 K . The results indicate that the surface area in genaral decreases with increasing platinum percentage, high platinum loaded (0.45% and 0.55%) it was found that the percent increasing in surface area was lower than those obtained for low platinum loaded catalysts , and at very higher platinum loading 0.6 %Pt , some reduction in surface area was
... Show MoreThe planning, designing, construction of excavations and foundations in soft to very soft clay soils are always difficult. They are problematic soil that caused trouble for the structures built on them because of the low shear strength, high water content, and high compressibility. This work investigates the geotechnical behavior of soft clay by using tyre ash material burnt in air. The investigation contains the following tests: physical tests, chemical tests, consolidation test, Compaction tests, shear test, California Bearing Ratio test CBR, and model tests. These tests were done on soil samples prepared from soft clay soil; tyre ash was used in four percentages (2, 4, 6, and 8%). The results of the tests were; The soil samples which
... Show MoreIn this paper, we consider the problem of stochastic project network when some or all activities are interrupted. An approach has been built to schedule the critical activities, by constructing some expressions based on the project lateness costs due to the interruption activities. Two simple example are presented to validate our approach.
Key words: Project Management, Project scheduling, Stochastic activity duration, Stochastic PERT.
Introduction
Recently, Projects planning and optimal timing, under uncertainty are extremely critical for many organizations, see [19]. Having an effective mathematical model wi
... Show MoreFilms of PMMA and copper sulphate doped PMMA have been prepared by casting method. Absorbance and transmittance spectra were recorded in the wavelength range (300-900) nm in order to calculate, single oscillator energy, dispersion energy, average oscillator strength, the refractive index at infinite wavelength, M-1 and M -3 moments of the optical spectra, it was found that all these parameters were effected by doping.
A colorectal polyp (CRP) is a growth on the lining of the colon or rectum. The incidence of CRPs is rapidly increasing with age. They are most often benign. The rectum is the most commonly affected site.
To determine the incidence, clinical presentation, and histopathologic types of CRP in Iraqi patients.
It is a cross-sectional screening study conducted in the medical c
The work is devoted to the study of the plastics features in modern construction use. The plastics classification in modern construction is generalized. This classification includes: the field of building products application, the features of the materials properties and products, a backup group that includes those products that are not included in the previous groups. The classification considered is the basis for choosing the basic materials properties that affect the quality and durability of products. To improve the plastics types in the construction, the Venn diagram is used. The main materials types for manufacturing a product of the "window profile" type are analyzed; the result of the studies is a comparative diagram.