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.
Background: Studying and investigating the transverse strength(Ts), impact strength(Is), hardness (Hr) and surface roughness(Ra) of conventional and modified autopolymerizing acrylic resin with different weight percentages of biopolymer kraftlignin, after curing in different water temperatures; 40°C and 80°C. Material and Methods: Standard acrylic specimens were fabricated according to ADA specification No.12 for transverse strength, ISO 179 was used for impact testing, Shore D for hardness and profilometerfor surface roughness. The material lignin first dispersed in the monomer, then the powder PMMA is immediately added. Ligninadded in different weight percentages. Then cured using pressure pot (Ivomet) in two temperatures;40°C a
... Show MoreThe aim of this research is to study the effect of welded joint design (Butt joint and lap joint) on thejoint strength during tension and fatigue loading with different current of welding (40,50,60,70,80) ^per, and different type of wire welding. The result of this research is showed that the effect of fatigue loading on the type of joint is more than the effect of tension loading on it. And the butt joint welding is better than the lap joint welding during the fatigue loaded.The experimental results of the effect of W'elding current showed that more increasing and more decreasing the value of the heat input, during the welding was found to produce mechanical brittleness on the buttjoint welding during the static and dynamic loading. Also i
... Show MoreThe research aimed to identify "the effectiveness of educational-learning design according to the model of brain compatibility in achievement among firstmiddle grade students in mathematics", in schools affiliated with the Second Karkh Directorate of Education. To achieve the goal of research, the following zero hypothesis has been formulated: " There is no statistically significant difference at the semantic level (05.0) between the average scores of experimental group students who will study with design accreditation (educational - learning) according to the brain compatibility model and the grades of control group students who will study in the usual way in the achievement thinking test". The research community, which is represented by
... Show MoreThe role of filamentous bacteria represented by Streptomycessp was studied as biological treatment for activated sludge AL- Restomia treatment unit in Baghdad city. The result shows reducing in phosphate concentration where apprise in started entrance the treatment unit 12.083 mg/L fast the unit stages reached to 8.426 mg /L where nitrate concentration apprises 3.59 mg/l and ending in 2.43 mg/L The concentration of ammonia apprises 1358 mg/L and reached to 140 mg/L. also the TDS concentration reduced from 1426 to 1203 mg/L where nutrient which represented (SO4, Mg, Ca, Na, K) reduced by range 30.883- 23.337 , 194- 121 , 440- 321 , 109.03- 101.53 and 16.85- 15.4mg/L respectively COD reduce from427.263- 82mg/L with absorbance0.018- 0.027
... Show MoreThis study evaluated the functional response of the larva of the predator Chrysoperla carnea by offering varying densities of cabbage aphid, Brevicoryne brassicae (L.) . Results showed conformity with type–II functional response, where the number of prey killed approaches asymptote hyperbolically as prey density increases (declining proportion of prey killed or the inverse density dependent) till it reached the stability stage determined by handling time and predator satiation. Also, the values of attack rate and handling time changed with age progress for both predator and prey. It has been observed an increase in the attack rate and reduction in handling time with the progress of the predator age when feeding on a particular nymphal in
... Show MoreThe study in duded isolation and identification of microbial isolates from oral cavity to 10 volunteers, diagnosed within the three groups: Staphylococcus aureus, Staphylococcus epidermidis, Streptococcus spp. and Candida albicans . The sensitivity test of all isolates bacteria Streptococcus spp. , S. aureus and S. epidermidis showed high resistance to Ampicillin(100)%,followed Methicillin (88.88)% and Amoxicillin / clavulanic acid(77.77)%, while the resistance for each of Vancomycin and Amoxicillin were (66.66)%, and the resistance to Erythromycin and Pencillin (55.55)% to each of them. The results showed less resistance to Trimethoprim (22.22)% and Cefalotine (11.11)% of all bacteria isolate. Investigation of the pre
... Show MoreABSTRACT Background: Color changes that are detectable to human eye can affect the esthetic appearance of ceramic veneers. The purpose of this study was to evaluate and compare the effect of artificial accelerated aging on the color of ceramic veneers cemented with different resin cements. Materials and Methods: Sixty discs were prepared with 0.5 mm thickness, 30 discs made from IPS e.max press (Ivoclar Vivadent) and 30 discs were made from VITA Enamic (VITA Zahnfabrik). The discs were cemented with three resin cements: Variolink Veneer MV 0 shade (Ivoclar Vivadent), Rely X veneer Translucent shade (3M ESPE) and NX3 Nexus Clear shade (Kerr Corporation) with 0.1 mm thickness. The spectrophotometer Easyshade Advance was used to measure the co
... Show MoreThe current research aims to determine the impact of the cognitive reconstruction program on the development of psychological hardness among middle school students through the experimental verification of three hypotheses. The research sample consisted of (16) out of (450) students selected from Ibn Rushud preparatory school- Al-Rusafa 2. These participants have been randomly distributed into two equal groups. The researcher has used the method of cognitive reconstruction with the experimental group, whereas with the controlling group, he used nothing. The researcher has further used the scale of psychological hardness of Kobassa with the participants; the scale has been built in a way that suits the sample of the study, which consisted
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