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.
The Ash'aris and their position on faith, An Ideological Study
Omed AbdulQader rasool
College of Islamic Sciences/Salahaddin University-Erbil
Abstract
The concept of faith is very complex, and there are a lot of talk about it among the major Islamic groups such as the Kharijites, the Mu'tazila, the Jahmiyya and others, because of its great importance, and the worldly and eschatological effects it entails according to the elements of faith such as recognition, ratification and action.
The researcher chose one sect, which is the
... Show MoreThis paper presents the application of a framework of fast and efficient compressive sampling based on the concept of random sampling of sparse Audio signal. It provides four important features. (i) It is universal with a variety of sparse signals. (ii) The number of measurements required for exact reconstruction is nearly optimal and much less then the sampling frequency and below the Nyquist frequency. (iii) It has very low complexity and fast computation. (iv) It is developed on the provable mathematical model from which we are able to quantify trade-offs among streaming capability, computation/memory requirement and quality of reconstruction of the audio signal. Compressed sensing CS is an attractive compression scheme due to its uni
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In fact, the main idea of the manuscript is to take note of a branch of Islamic jurisprudence, which is the science of jurisprudential jurisprudence and this manuscript in its title and subject to the men of knowledge of jurisprudence because of its ambiguity calls for thinking, and the brainstorming mood to test the intelligence of jurisprudence, Of students of knowledge jurisprudence. This section contains (28) questions starting with the question (72) and ending with (100
These Chapters are concerning a lot of information about Islamic conquest of Egypt . The important chapters are the following :- Chapter 111 :- Concerning the first encounter of Amru with the Romans at the city of Heliopolis . Chapter 112:- How all the Jews assembled in the city of manuf owing to their fear of the Muslim . the Jews left the gates of Misr open and fled to Alexandria .
In fact, the main idea of the manuscript is to take note of a branch of Islamic jurisprudence, which is the science of jurisprudential and this manuscript in its title and subject to the men of knowledge of jurisprudence because of its ambiguity calls for thinking, and the brainstorming mood to test the intelligence of jurisprudence, Of students of knowledge jurisprudence. This section contains (25) questions starting with the question (101) and ending with (125) .
In this research was the study of the educational values when Shafei, contained in hair Shafi'i, and that what the role of these values in the education of generations, and the possibility of their application in the educational curriculum. Find addressed Shafei life and his time. The values derived from his hair, as well as quoting from the Koran and influenced by it, which is evident in the hair, governance and eating Alomthal.okzlk Find the importance of this thought in modern education, so as to realism and ease of application. It is the search results, the Shafi'i put thought educationally integral based on the Koran rise to the level of theory. Find and conclusions: that education in its present situation
... Show Moreتم التحري عن انتاج انزيم الكايتنيز من خميرة Saccharomyces cerevisiae حيث زرعت هذه الخميره في وسط سائل يحتوي على الكايتين ومواد نتروجينية مختلفة . اجريت غربلة لسلالات الخميرة المستعملة لتعين السلالة الاعلى انتاجا للانزيم . بينت النتائج ان السلالة S2 اعطت اعلى فعالية نوعية بلغت 3.5 وحدة /ملغم بروتين .
This paper describes a microcontroller-based function generator system. By the function generator sine wave, square wave, quasi-square wave, saw-tooth and triangular waveforms are generated over a wide frequency range according to user requirements. By utilizing processing capabilities of the microcontroller the hardware is minimized exceedingly. The output waveform shapes are digitally-controlled to achieve the required wave shape. The single chip microcomputer of waveform generation equipment offers the possibility of improvements in manufacture reliability, maintenance and servicing and increased control flexibility. The system is built and tested. The results of test were satisfactory and appreciated by test engineers at different ce
... Show MoreEconomic life in any of the countries depends mainly on economic activity due to its great role in meeting the needs and expenditures of the state . therefore ، Bahrain played a major role in commercial exchange operation ، whether at home or abroad . whatever the matter