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.
يهدف البحث الحالي إلى الاستفادة من القهوة المستهلكة , كمادة وسيطة حيث تعد القهوة المستهلكة من المخلفات المضرة للبيئة الاستخراج الكافيين الطبيعي والذي يعد مادة ذات نشاط حيوي واهمية, وتحديد العوامل الفعالة في كفاءة عملية الاستخلاص من حيث تركيز الكافيين. تضمنت المتغيرات الرئيسية المدروسة وقت الاستخلاص 0-150 دقيقة ، ودرجة الحرارة 25-55 درجة مئوية ، وسرعة الخلط 180-450 دورة في الدقيقة ، ودرجة الحموضة العالق
... Show MoreThe risk of breast cancer development is believed to be attributed to the alterations of a number of key biological components. Within this context, elevated levels of some chemokines that act as growth factors and can promote cancer development. The current study was designed to evaluate CXCL3 (a chemokine C-X-C Motif Ligand 3) and leptin (a peptide hormone synthesized by adipose tissue with cytokine activity) serum of Iraqi breast cancer patients in comparison to healthy controls. A total of 90 participants consisted of 60 patients diagnosed with breast cancer and 30 healthy women as control group were enrolled into this case-control study. Venous blood samples were collected from all participants to evaluate CXCL3 and leptin serum levels
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