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.
DBN Rashid, 2012 - Cited by 2
Erosion and deposition are natural phenomena in the river estuaries that could be presented as a dynamic process involving removing materials from one location and accumulating these materials at other locations. These two phenomena may cause changes in waterways and affect offshore structures. The Shatt Al-Arab River Estuary, Iraq was greatly affected by these two phenomena, and topography changes occurred. Velocity profiles and bed shear stress can be used as indicators to identify the erosion and deposition locations. Large-scale roughness elements proved to make beneficial changes in the hydraulic properties of open channels. They can create desirable effects to control erosion
Subsurface soil water retention (SWRT) is a recent technology for increasing the crop yield, water use efficiency and then the water productivity with less amount of applied water. The goal of this research was to evaluate the existing of SWRT with the influence of surface and subsurface trickle irrigation on economic water productivity of cucumber crop. Field study was carried out at the Hawr Rajab district of Baghdad governorate from October 1st, to December 31st, 2017. Three experimental treatments were used, treatment plot T1 using SWRT with subsurface trickle irrigation, plot T2 using SWRT with surface trickle irrigation, while plot T3 without using SWRT and using surface tickle irrigation system. The obtained results showed th
... Show MoreEarth dams in regions with moderate to high seismic activity are crucial for protecting downstream communities. Iraq and its neighboring areas have seen recurrent seismic activity, notably the 2017 Halabja Earthquake, which potentially compromised the integrity of the existing earth dam. The Darbandikhan Dam, affected by an earthquake, has inadequacies in its crest and downstream slope, presenting a greater danger of significant earthquake-induced damage compared to cyclic shocks. Consequently, evaluating the dam's safety is essential for safeguarding downstream residents and identifying optimal ways to avert slope stability failure amid recurrent seismic activity. Iraq's seismicity map is being updated to reflect earthquake magni
... Show MoreThis study aims to examine the technologies of education and their importance, shedding light on their reality and status in Sudan especially in the secondary stage. It has become necessary to invest these technologies and include them in different aspects of the technical education curricula. Such a step helps cope with the innovative scientific development in the advanced countries, qualify professors and technicians, develop the factories and workshops, and create an attractive technical educational environment to the pupils. Thus, the researcher has adopted a descriptive analytical approach that is based on conducting pilot visits to certain technical schools in Al-Khartoum state. Different aspects of such schools were examined
... Show MoreBackground: Consanguineous marriage is a relationship between biologically related individuals. Genetic factors have a role in gene environment interactions that takes the center stage. The evidence of oral disease (gingivitis and periodontitis) may depend on genetic syndromes, inherited diseases, familial studies etc. The present study aims at assessing dental plaque and gingival health condition in children of inbreeding parents compared with children of outbreeding parents among primary schools in Al-Qasem city/ Babylon governorate in Iraq. Materials and methods: this comparative study included three hundred ninety eight (398) students, 6-12 years old, from 4 primary schools; 199 children had their parents of inbreeding marriage with
... Show MoreThe aim of the research is to demonstrate the impact of organizational diversity management on achieving success, The problem of research is to create an appropriate work environment that stimulates everyone regardless of each dimension of diversity, So as to reach the best levels of success, The importance of research is to identify how the organization in question can manage organizational diversity effectively and contribute to its success, The research started from two main hypotheses which were derived from sub-hypotheses to identify the correlation and influence between the search variables by analyzing the answers of the research sample which included (81)
... Show MoreIn this article we study the variance estimator for the normal distribution when the mean is un known depend of the cumulative function between unbiased estimator and Bays estimator for the variance of normal distribution which is used include Double Stage Shrunken estimator to obtain higher efficiency for the variance estimator of normal distribution when the mean is unknown by using small volume equal volume of two sample .
The current research aims to identify the time-management skills based on the post-test of the experimental group as well as to examine the effect of a training program on developing the skills of managing time among the study sample. To achieve the research objectives, the researcher designed a scale of time management skill included (30) paragraphs. The research reached that the training program is significantly effective in managing and organizing time. There are statistically significant differences in pre-posttest between the experimental and control groups.