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.
Abstract:
We can notice cluster data in social, health and behavioral sciences, so this type of data have a link between its observations and we can express these clusters through the relationship between measurements on units within the same group.
In this research, I estimate the reliability function of cluster function by using the seemingly unrelate
... Show MoreIn this study, concentrations of radon and uranium were measured for twenty six samples of soil. The radon concentrations in soil samples measured by registrant alpha-emitting radon (222Rn) by using CR-39 track detector. The uranium concentrations in soil samples measured by using registrar fission fragments tracks in CR-39 track detector that caused by the bombardment of U with thermal neutrons from 241 Am-Be neutron source that has flux of 5 ×103n cm-2 s-1.
The concentrations values were calculated by a comparison with standard samples The results show that the radon concentrations are between (91.931-30.645Bq/m3).
The results show that also the uranium concentrat
The education sector suffers from many problems, including the scarcity of schools that can absorb the increasing number of students in light of the increasing population growth rate, as some regions suffer from a lack of opening of new schools or the expansion of existing schools to increase their capacity so that attention is required. The research sought to identify the level of maturity of project management at the research site (Building Department in Al-Karkh I/ Ministry of Education) Being responsible for educational projects and their implementation and to know that, the ten areas of the knowledge guide to project management PMBOK have been adopted according to the PM3 model (one of the models of maturity
... Show Moreantimicrobial solutions against Coliforms, E. coli O157: H7, yeasts and molds were evaluated by agar well diffusion method. Chitosan (CH) exhibited best antimicrobial activity against the treated microorganisms at concentration of (5%) with contact time for 6hrs at refrigeration temperature (4ÚC), zones of inhibition for (GA) and (CH) for each solution alone ranging from (0 to 10 mm), chitosan solution (CH) exhibited both antibacterial and antifungal activities, Gum Arabic washing solution showed significant antibacterial activity (P < 0.05) against the microorganisms at concentration (15%), without inhibitory effect against E. coli O157:H7 at concentration (10%), in the current study the results confirmed that (15%) (w/v) of GA and 5%
... Show MorePushover analysis is an efficient method for the seismic evaluation of buildings under severe earthquakes. This paper aims to develop and verify the pushover analysis methodology for reinforced concrete frames. This technique depends on a nonlinear representation of the structure by using SAP2000 software. The properties of plastic hinges will be defined by generating the moment-curvature analysis for all the frame sections (beams and columns). The verification of the technique above was compared with the previous study for two-dimensional frames (4-and 7-story frames). The former study leaned on automatic identification of positive and negative moments, where the concrete sections and steel reinforcement quantities the
... Show MoreThe objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the <
... Show MoreThe research aims to identify the role of strategic improvisation as an independent variable with its dimensions (Building the Solution, Intuition, Adaptation, and Spontaneity) and the Entrepreneurial Orientation as a dependent variable with its dimensions (Identifying Opportunities, Creativity, Adopting risk, and Vision). This research has been applied in the Rafidain Bank and its branches (Sunk, People, Al-Firdaws, and Alawiya); it used the questionnaire as a basic tool for collecting information. The sample was intentionality, which included all the heads of departments in the bank’s branches, which amounted to (33) workers, and data on the questionnaire paragraphs of 28 were processed using the SPSS V.23 and AMOS V.23). The most impor
... Show MoreBackground: Breast lump is one of the most common prevalent complaint of patients attending breast clinics.
Objective: To determine if there is any change in the pattern of common breast, diseases presenting as breast lumps between pregnant and non-pregnant women among patients attending Al-Elwiya Breast Clinic.
Methods: This is a cross – sectional study, with convent's patient sampling setting in AL-Elwiya Breast Cancer Early Detection Clinic from 1st Feb. to 1st May 2018, we collected data from patients with breast lumps including the age groups, pregnancy status, parity status, previous breast diseases, hormonal drugs, menstrual cycle, breast fe
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