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 simple setup of random number generator is proposed. The random number generation is based on the shot-noise fluctuations in a p-i-n photodiode. These fluctuations that are defined as shot noise are based on a stationary random process whose statistical properties reflect Poisson statistics associated with photon streams. It has its origin in the quantum nature of light and it is related to vacuum fluctuations. Two photodiodes were used and their shot noise fluctuations were subtracted. The difference was applied to a comparator to obtain the random sequence.
The present work involved designing and synthesizing of a series of new. compounds which their molecules are composed from two biologically active components namely sulfamethoxazole or β-lactam containing drugs and cyclic imides. The target new compounds were synthesized by two steps in the first one a series of six bis (N-drug phthalamic acid_4-yl) ketone (1-6) were prepared from the reaction of sulfamethoxazole or β-lactam containing drugs with benzophenone 3, 3′, 4, 4′ -tetracarboxylic dianhydride.
In the second step, compounds (1-6) were introduced in dehydration reaction via fusion process producing the target compounds bis (N-drug phthalimidyl-4-yl) ketone (7-12). The antibacterial and antifungal high
... Show MoreThis paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers which is defined by has a lower bound in terms of . This bound is more sharper than Mangenstern bound when Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all
The researcher tried to show the importance of using environmental taxes as an effective economic factor for reducing contaminators resulting from cars exhausts, and presenting a suggested pattern for environmental taxes as a nucleus and a starting point for a wider implementing of environmental taxes in Iraq. &nbs
... Show Moreي لا ماق ثحبلا فادهأ قيقحتلو ثحبلا ةنيعل نايبتسا ءارجاو فراصملل ةيلاملا مئاوقلا ليلحتب ثحاب اهمهأ ناك تاجاتنتسا ىلإ ثحابلا لصوت دقو لإ صاخ معد دوجو مدع نم ةيفرصملا رطاخملا ةراد ةروصب اهدوجو مدعو فراصملل ةماعلا تارادلاا يف اهدوجو رصتقي ثيح ،ايلعلا تاهجلا لبق نم ديزي امم ،عورفلا يف ةلاعف مدع ةجيتن عورفلا نم ةدلوتملاو فراصملا اههجاوت يتلا رطاخملا اهمهأ ناك تايصوت ىلإ ثحابلا لصوت دقو امك ،ةيفرصملا تلاماعم
... Show MoreThe research revolves around the methodology of the historian Ibn Wasil
(d.697 AH) in dealing with the Mongolian invasion through his book
“Mafrej al-Karroub fi Akhbar Bani Ayyub