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.
Recently, Social Sustainability has gained significant value as it was considered by the late studies as a principal dimension along with the environmental and economic sustainability. And because of, on the other hand, the significant social role of the school for forming the student’s personality, this research is an appeal for rehabilitating and promoting Iraqi Schools according the issue of social sustainability.As there is no evaluation for the Iraqi Schools, the research is dedicated to this problem, aiming to carry out the stated evaluation and define the design treatments needed for the rehabilitation process. To achieve this goal, a theoretical background for the concept of social sustainability, its criteria, the school and i
... Show MoreProchloperazine maleate (PCM) is one of the most prescribed phenothiazine. The purpose of the present research was to develop fast dissolving tablets of PCM with β-cyclodextrin inclusion complex. Tablets prepared by wet granulation with sublimation and by using different superdisintegrants type [ low-hydroxypropylcellulose LH21 (L-HPC LH21), carboxymethylcellulose calcium (ECG505), crospovidone (CP)], and different type of subliming agents (urea and ammonium bicarbonate (AB)). Tablets evaluated for its % friability, disintegration time, wetting time, hardness, content uniformity, weight variation, in vitro dissolution studies. For further enhancement of disintegration and dissolution, PCM orodispersible tablet were formula
... Show MoreSix species of aquatic snails were sorted from three sites, the irrigation canal of Baghdad University campus (S1), River Tigris at Al-Za'afaraniah district / Baghdad(S2) , and River Euphrates at Al-Haideriah district Al-Najaf province(S2). The species included Melanopsis nodosa ;Melanoides tuberculata ; Thaiodaxsas jordani ; Lymnaea auricularia ; Physa acuta and Bellamya bengalensis. The first specis recorded the highest total number and was found in high density in the R. Euphrates site (S3), while the last species was the most widely distributed species, and found in all study sites. The last three species were found in Tigris river (S2) , while the first and last species were collected from the irrigation canal (S1).The result reveal
... Show MoreConstruction and operation of (2 m) parabolic solar dish for hot water application were illustrated. The heater was designed to supply hot water up to 100 oC using the clean solar thermal energy. The system includes the design and construction of solar tracking unit in order to increase system performance. Experimental test results, which obtained from clear and sunny day, refer to highly energy-conversion efficiency and promising a well-performed water heating system.
Praise be to God, Lord of the worlds, and the best of prayers, and the completion of the blessing of our master Muhammad Al-Hadi Al-Amin, his family and companions, the righteous and those who followed his path and guided him to the day of judgment.
And after:
It is God's human honor that he has legalized marriage and made optimal goals and intentions for her:
1 establish a safe and reassuring life between the husband and his wife based on the tranquility and love and compassion is achieved through satisfying the instincts of the road project from the verse: and that He created for you mates from among yourselves to find repose in them and put between you affection and mercy in this are Signs for those who reflect ()
The rapid increase in the number of older people with Alzheimer’s disease (AD) and other forms of dementia represents one of the major challenges to the health and social care systems because of a large number of people affected. Early detection of AD makes it possible for patients to access appropriate services and to benefit from new treatments and therapies, as and when they become available, and to plan for the future. The onset of AD starts many years before the clinical symptoms become clear. A biomarker that can measure the brain changes in this period would be useful for early diagnosis of AD. Potentially, the electroencephalogram (EEG) can play a valuable role in early detection of AD. Damage caused to the brain due to AD leads t
... Show MoreThe synchronization of a complex network with optoelectronic feedback has been introduced theoretically, with use of 2×2 oscillators network; each oscillator considered is an optocoupler (LED coupled with photo-detector). Fixing the bias current (δ) and increasing the feedback strength (Ԑ) of each oscillator, the dynamical sequence like chaotic and periodic mixed mode oscillations has been observed. Synchronization of unidirectionally coupled of light emitting diodes network has been featured when coupling strength equal to 1.7×10-4. The transition between non-synchronization and synchronization states by means of the spatio-temporal distribution has been investigated.
Characteristic of money laundering phenomenon is a compound and complex nature like the style of regular crimes . These operations are planned and excuted with those who have high quality experiences to hide the evidences of their deeds so They ask the help of financials ,economicals and legists to plan for money laundering. Banks are important and suitable places for illegal circulation of money because of the different types of accounts , rapidity and overlap which emphasis of its main duty to dislocate illegal money which comes from illegal sources without adding legal characteristic to it . Here we should explain the important role of banks in striving the phenomenon –Bank should try to show and analyze inward proced
... Show MoreThis research deals with a unique and innovative topic, that is the study of complaint in the Quranic text. Despite its importance, it has never been studied before, because most of the complaint 's meanings in the Quranic text is: the in explicit complaint. The mentioned complaint's expressions in different contexts overlap with other purposes, in particular call method and its peripherals like mourn , ask for help , exclamation and others.
Moreover, expressions that reveal complaint are related to the complainant's emotional and psychological status, and the complaint's context.
This research deals with the topic into two sections: The first deals with the important expression of complaint such as: iff, ouah, mooing, crying. The