Бидний тухай
Багш ажилтан
One of the numerous methods for evaluation is defining criteria aligned with objectives and assessing them with points. Employing systematic and reliable tools to evaluate based on multiple criteria of varying importance is crucial for achieving desired goals. Moreover, they significantly influence the outcome of the research. In our research, we consider the methodological aspects of the Analytical Hierarchy Process (AHP) as a means of evaluating teachers' work. In Mongolia, as part of our efforts to enhance teacher quality, we're in the midst of implementing performance evaluations for the second time. Recognizing the need for refinement and updating, we aim to evaluate the multidimensional teachers' work, considering various factors such as location and professional nuances. Our endeavor is to craft a comprehensive evaluation framework that accurately reflects the multifaceted roles and responsibilities of teachers. We've provided an example by defining just one criterion for evaluating teachers' work, along with its corresponding sub-criteria. Additionally, we've showcased qualitative and quantitative analyses, as well as the development of software applications aimed at facilitating the implementation of the AHP method. Through our research, we aspire to showcase the potential of research-driven decision-making and foster broad-scale collaboration among evaluation experts, researchers and policymakers. Түлхүүр үг: АШП арга, олон хүчин зүйлийн анализ, багшийн үнэлгээ
Abstract: The concept of the Sombor indices of a graph was introduced by Gutman. A vertex-edge variant of the Sombor index of graphs is called the KG-Sombor index. Recently, the Sombor and KG-Sombor indices of Kragujevac trees were studied, and the extremal Kragujevac trees with respect to these indices were empirically determined. Here we give analytical proof of the results. Keywords: Sombor index, KG-Sombor index, Kragujevac tree AMS Subject classi cation: 05C35, 05C09, 05C90, 05C92
МУИС-д 1960-аад оны сүүлчээр Тооцон бодох математикийн анхны лекцүүдийг Киевийн их сургуулийн профессорууд уншиж байсан тэр цаг үеэс эхэлсэн математикийн энэ салбар Moнгол улсын ууган шавь сургуулиудын нэг болон эрчимтэй хөгжиж иржээ. Ѳнөөдрийг хүртэлх тавь гаруй жилийн хугацаанд МУИС-иас Тооцон бодох математикийн чиглэлээр үндэсний эрдэмтэн, судлаачид олноор төрөн гарч, тэдний бүтээл дотоод, гадаадын мэргэжлийн өндөр түвшний сэтгүүл, монографад хэвлэгдэж, бусад орны судлаачдын бүтээлүүдэд эшлэгдэж байна. Манай эрдэмтэн, багш нар сурах бичиг эх хэл дээрээ бичиж, бакалаврын оюутнуудаа мэргэшүүлэн сургаж, ахисан түвшний судлаачдаа удирдан ажиллаж, төрөл бүрийн судалгааны төсөл хөтөлбөрүүдийг хэрэгжүүлж ирсний үр дүнд Тооцон бодох математик нь математикийн бусад салбаруудтай төдийгүй бусад шинжлэх ухаан, технологи, үйлдвэрлэлтэй нягт холбоотой хөгжиж байгаа билээ. Үүний нэг тод жишээ гэвэл сүүлийн үед манай судлаачдын эрдэм шинжилгээ, судалгааны үр дүн олон салбар, чиглэлийн дундын бүтээл болон гарч байна. Энэхүү өгүүллээр зөвхөн МУИС-ийн Тооцон бодох математикийн онолын судалгааг илүү тодотгохын зорьж, судалгааны голлох үр дүнгүүдийн тухай товч танилцуулсан болно.
The graph invariant RM2, known under the name reduced second Zagreb index, is defined as RM2(G)=∑uv∈E(G)(dG(u)−1)(dG(v)−1), where dG(v) is the degree of the vertex v of the graph G. In this paper, we give a tight upper bound of RM2 for the class of graphs of order n and size m with at least one dominating vertex. Also, we obtain sharp upper bounds on RM2 for all graphs of order n with k dominating vertices and for all graphs of order n with k pendant vertices. Finally, we give a sharp upper bound on RM2 for all k-apex trees of order n. Moreover, the corresponding extremal graphs are characterized.
Abstract Let G(V, E) be a graph with vertex set V and edge set E. The ve-degree of a vertex v\in V equals the number of edges ve-dominated by v and the ev-degree of an edge e\in E equals the number of vertices ev-dominated by e. Recently, Chellali et al. studied the properties of ve-degree and ev-degree of graphs (Chellali et al., 2017). Also they focused on the regularity and irregularity of these types of degrees and proposed several open problems. In this paper, we solve one of them and obtain some results on the regularity and irregularity of ve- and ev-degrees in graphs.
