1. RBL-STEM learning activity framework: Improving students combinatorial thinking skills for solving image encryption problem using edge irregular reflexive k-labeling.
- Author
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Marsidi, Dafik, Susanto, and Kristiana, Arika Indah
- Subjects
IMAGE encryption ,UNDIRECTED graphs ,PROBLEM solving ,LEARNING ,QUALITATIVE research ,WEIGHTED graphs - Abstract
Combinatorial skills refer to the ability to analyze and manipulate combinations of elements or objects in various ways to solve problems or achieve specific goals. These skills involve understanding how different elements can be arranged or combined to create new outcomes, often systematically and organized. In this era, these skills should be endorsed in the classroom so that the young generation possesses these skills. However, in reality, students' combinatorial thinking skills still need to improve since the learning model applied in the classroom has yet to foster these skills. The indicators of combinatorial thinking consist of e identifying some cases, recognizing patterns from all cases, generalizing all cases, proving mathematically, and considering other combinatorial problems. This paper will describe the learning activities of RBL-STEM to improve students' combinatorial thinking skills in solving the edge irregular reflexive 푘-labelling problem and its application in image encryption. Let 퐺 be a connected, simple, and undirected graph with a vertex set 푉(퐺) and an edge set 퐸(퐺).A total 푘-labeling is an edge irregular total 푘-labeling of the graph G if even two distinct edges have different weights. The edge weight is the sum of the labels of its incident vertices and the labels of that edge. Bac̆a extended the above notion into an edge irregular reflexive 푘-labeling. The total 푘-labeling defined the function 푓
e : 퐸(퐺)→{1,2,3, ..., 푘e } and 푓v : 푉(퐺)→{0,2,4, ..., 2푘v } where 푘 = 푚푎푥{푘e , 2푘v }. For the graph G, the total 푘-labeling is called an edge irregular reflexive 푘-labeling if the condition every two different edges 푥1 푥2 and 푦1 푦2 of 퐺, 푤푡(푥1 푥2 )≠푤푡(푦1 푦2 ), where 푤푡(푥1 푥2 ) = 푓v (푥1 ) + 푓e (푥1 푥2 ) + 푓v (푥2 ). The smallest value of 푘 for which such labelling exists is called the reflexive edge strength of the graph 퐺, denoted by 푟푒푠(퐺). This research uses a qualitative narrative approach, starting with developing a prototype of the application in image encryption using edge irregular reflexive 푘 labelling and continuing with formulating the stage of learning activities regarding RBL-STEM. The results of this research are in the form of an RBL-STEM learning framework consisting of six stages of learning activities. Based on these results, the following steps will be the development of RBL-STEM maker-space learning materials. [ABSTRACT FROM AUTHOR]- Published
- 2024
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