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 research problem can be summarized through focusing on the environment that surrounds students and class congestion, how these factors affect directly or indirectly the academic achievement of students, how these factors affect understanding the scientific material that the student receives in this physical environment, how classroom’s components such as seats, space With which the student can move, the number of students in the same class, the lighting, whether natural or artificial, and is this lighting sufficient or not enough, the nature of the wall paint old or modern, is it comfortable for sight, the blackboard if it is Good or exhausted, In addition to air-conditioning sets in summer and winter, this is on the on
... Show MoreRecently, some prostate cancer patients have acquired resistance to the second -generation drugs (anzalutamide and apalutamide) prescribed for the treatment of this disease due to the emergence of the F876L mutation, which represents a challenge to modern medicine. In this study, a new series of 2-thiohydantoin derivatives were prepared through the reaction of different derivatives of maleimide (1c-4c) with isothiocyanate derivatives. The prepared compounds were diagnosed using FT-IR,1H-NMR ,13C-NMR, Mass spectra. The prepared series compounds has been studied against prostate cancer cells. The MTT assay was used to determine the activity of the prepared compounds against prostate cancer cells. The da
... Show MoreUnited nation determined many basic climatic effects which affect the crust of Earth.
And the most important one is the climatic change and its effect on environmental, economic,
social, and political effects. So, the amount of rain which is considered as one of climatic
changes in Iraq should be studied.So, this research explains the factors which affect rain, its
overall average, the variation in the amounts of rain, the amount of yearly rain and variation
in both yearly and monthly rains by using standard variation and yearly fluctuation.As a
result, it is concluded that the number of rainy days doesn't mean an increase in rains amount.
And there's variation in rains amount in all study areas which is contrastive
In this paper, the Normality set will be investigated. Then, the study highlights some concepts properties and important results. In addition, it will prove that every operator with normality set has non trivial invariant subspace of .
Abstract
In order to enhance the efficiency of flat plate solar water collectors without changing in its original shape and with low additional cost, twisted strips are inserted inside its riser pipes. Three flat plate collectors are used for test. Family of twisted strips are inserted inside each collector risers with different twisted ratios (TR=3,4,5). The collectors are connected in parallel mode (Z-Configuration) and are exposed to the same conditions (solar radiation and ambient temperature) .The experimental results show that, the highest heat transfer rate occurs at twisted ratio (3) .Consequently, for the same twisted ratio the daily efficiencies for the solar collector at d
... Show MoreReceipt date:3/13/2021 accepted date:5/26/2021 Publication date:12/31/2021
This work is licensed under a Creative Commons Attribution 4.0 International License.
energy is one of the strategic resources within international politics, and this is through the existing competition between the international powers on it, and the global powers have begun to rely on interest in new areas, such as import, depending on new projects an
... Show MorePraise be to Allaah.
My research has included the following: The field of application of semantics when fundamentalists are the book and the Sunnah. Imam Ibn Hajar agreed with the majority of fundamentalists that what is meant from the year (one word denotes one side on two things onwards), and agreed that the significance of the year specific to the rest of its members is not a definite and definite formulas of the public has the singular known as (the) Astragharism, and the plural known as ( The nationality stating that dumping, pluralism is defined as (add), and nakra, if it occurs in the context of the condition, denial and prohibition, the names of the condition, the connected names, and the word (all - all). And the year in whic
The sole aim of the tribe of the Messenger of Allah (PBUH) and his basilica was to revoke the Umayyad heresy and to refute the suspicions through which they climbed to the top of the pyramid of power and legitimized the leadership of Muslims (heresy of hereditary rule) with the sword and blood. Therefore, Imam Hussein (peace be upon him) began his Ashura process with his short divine message in its words and great in its vocabulary and content and even the future of Mohammedan Islam over the times and spaces - what we will see in the folds of research, God willing.
Activated carbon was Produced from coconut shell and was used for removing sulfate from industrial waste water in batch Processes. The influence of various parameter were studied such as pH (4.5 – 9.) , agitation time (0 – 120)min and adsorbent dose (2 – 10) gm.
The Langmuir and frandlich adsorption capacity models were been investigated where showed there are fitting with langmmuir model with squre regression value ( 0.76). The percent of removal of sulfate (22% - 38%) at (PH=7) in the isotherm experiment increased with adsorbent mass increasing. The maximum removal value of sulfate at different pH experiments is (43%) at pH=7.