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.
A total of 247 specimens of the Mallard were collected from Baghdad city and kut City and 154 specimens the collection was started from October1999
Conservation of Concept among Children: Semantic Study
This work comprises the synthesis of new thioxanthone derivatives containing C-substituted thioxanthone. To obtain these derivatives, the o-mercapto benzoic acid was chosen as the starting material, which was reacted with dry benzene in sulfuric acid (98 %) to produce the thioxanthone (1). The 2,7-(disulfonyl phosphine imine) thioxanthone (4-8) were prepared from reaction of compound (1) with chlorosulfonic acid gave 2,7-(disulfonyl chloride) thioxanthone (2). Treatment of (2) with sodium azide to produce 2,7-(disulfonyl azide) thioxanthone (3). Condensation of (3) with phosphorus compounds afforded compounds (4-8). The 2,7-(disulfonamide) thioxanthone (9-21) was obtained when co
... Show MoreThis research was aimed to study the pollen morphology for the genus Pterocephalus(Vaill) from Dipsacaceae family in Iraq, and to utilize these feathers in isolating the species as valuable taxonomic traits for enriching Iraqi flora. The study included characteristics of the type, shape, size, sculpturing and apertures, as well as determining the full dimensions using light microscopy as well as numerical analysis of this species and draw polygonal shapes and denderogram convergence between species. The results of the study of pollen and polygonal forms showed significant differences in the characteristics at the level of each species, which helps to identification the genus species, as it was found that the pollen was a tricolp
... Show MoreOptical detector was manufactured Bashaddam thermal evaporation technique at room temperature under pressure rays studied characteristics of reactive Scout efficiency quantitative ratio of the signal and the ability equivalent to noise
It is axiomatic that languages mirror the world view of their users. Manipulating honorific forms among people inevitably reflects this truth . Honorifics are conventionalized forms or expressions manifested in all the world's languages and are used to express the social status of the participants in the verbal interaction and to convey indications like politeness and respect . English is no exception. However the question is what exactly creates these forms and their meanings. Although honorifics have been extensively researched from a grammatical and semantic angle , yet they haven’t received that significant attention i
... Show MoreIn this thesis, we introduced some kinds of fibrewise topological spaces by using totally continuous function is called fibrewise totally topological spaces. We generalize some fundamental results from fibrewise topology into fibrewise totally topological spaces. We also introduce the concepts of fibrewise totally separation axioms, fibrewise totally compact and locally totally compact topological spaces. As well as fibrewise totally perfect topological spaces. We explain and discuss new notion of fibrewise topological spaces, namely fibrewise totally topological spaces. We, also introduce the concepts of fibrewise totally closed topological spaces, fibrewise totally open topological spaces, fibrewise locally sliceable and locally s
... Show MoreIn this work, the linear properties of Vitamin D3-5000IU soft gel were investigated by measuring its absorption and fluorescence spectra. It was observed that there was a shift towards longer wavelength within limits (75 nm), with quantitative efficiency equal to (33.58%). The values of absorbance were used to calculate the extinction coefficient, optical refractive index, optical conductivity and optical dielectric constant values.
The non-linear properties of Vitamin D3-5000IU soft gel was also studied using the Z-Scan technique by using Neodymium-doped Yttrium Garnet (Nd: YAG) continuous laser (CW) emitting in &n
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