Graph Theory for Primary School Students with High Skills in Mathematics

Graph theory is a powerful representation and problem-solving tool, but it is not included in present curriculum at school levels. In this study we perform a didactic proposal based in graph theory, to provide students useful and motivational tools for problem solving. The participants, who were highly skilled in mathematics, worked on map coloring, Eulerian cycles, star polygons and other related topics. The program included six sessions in a workshop format and four creative sessions where participants invented their own mathematical challenges. Throughout the experience they applied a wide range of strategies to solve problems, such as look for a pattern, counting strategies or draw the associated graph, among others. In addition, they created as challenges the same type of problems posed in workshops. We conclude that graph theory successfully increases motivation of participants towards mathematics and allows the appearance and enforcement of problem-solving strategies.

Concepts on Coloring of Cluster Hypergraphs with Application

Coloring of graph theory is widely used in different fields like the map coloring, traffic light problems, etc. Hypergraphs are an extension of graph theory where edges contain single or multiple vertices. This study analyzes cluster hypergraphs where cluster vertices too contain simple vertices. Coloring of cluster networks where composite/cluster vertices exist is done using the concept of coloring of cluster hypergraphs. Proper coloring and strong coloring of cluster hypergraphs have been defined. Along with these, local coloring in cluster hypergraphs is also provided. Such a cluster network, COVID19 affected network, is assumed and colored to visualize the affected regions properly.

Implementasi Algoritma Sequential dan Welch Powell pada pewarnaan graf (studi kasus pewarnaan peta kota Makassar)

The aim of this research is how to implement Sequential algorithm and Welch Powell algorithm on graph coloring, especially on Makassar city map coloring. The research method used was a case study aimed at searching information in the form of a map of Makassar city. The first step is to take a colored map of Makassar city at the Dinas tata ruang kota makassar, then redraw it with the help of Corel Draw X7 software, so there are no colors. The next step is to represent the map in graph form by taking the region (sub-district) as a node and then doing graph coloring using Sequential algorithm and Welch Powell algorithm. The results of coloring the Makassar city map using Sequential algorithm and Welch Powell algorithm, both produce chromatic numbers χ (G) = 4 or the number of colors produced to color a graph there are 4 colors. The colors used are red, yellow, green and blue. Then from the results of coloring this graph can easily be applied to color the map of the city of Makassar based on the coloring requirements obtained. Because it has the same chromatic numbers, it can be concluded that the Sequential algorithm is no better than the Welch Powell algorithm, or vice versa the Welch Powell algorithm is no better than the Sequential algorithm for the case of coloring the Makassar city map. The previous Makassar city map coloring or without the algorithm, produces chromatic numbers χ (G) = 12 or the number of colors produced to color a graph there are 12 colors. So that the two algorithms are much better at coloring than the previous Makassar city map coloring or without the algorithm

Region Coloring in Minahasa Regency Using Sequential Color Algorithm

Graph Theory is one of the mathematical sciences whose application is very wide in human life. One of theory graph application is Map Coloring. This research discusses how to color the map of Minahasa Regency by using the minimum color that possible. The algorithm used to determine the minimum color in coloring the region of Minahasa Regency that is Sequential Color Algorithm. The Sequential Color Algorithm is an algorithm used in coloring a graph with k-color, where k is a positive integer. Based on the results of this research was found that the Sequential Color Algorithm can be used to color the map of Minahasa Regency with the minimum number of colors or chromatic number χ(G) obtained in the coloring of 25 sub-districts on the map of Minahasa Regency are 3 colors (χ(G) = 3).

Bin2Vec: A Better Wafer Bin Map Coloring Scheme for Comprehensible Visualization and Effective Bad Wafer Classification

A wafer bin map (WBM), which is the result of an electrical die-sorting test, provides information on which bins failed what tests, and plays an important role in finding defective wafer patterns in semiconductor manufacturing. Current wafer inspection based on WBM has two problems: good/bad WBM classification is performed by engineers and the bin code coloring scheme does not reflect the relationship between bin codes. To solve these problems, we propose a neural network-based bin coloring method called Bin2Vec to make similar bin codes are represented by similar colors. We also build a convolutional neural network-based WBM classification model to reduce the variations in the decisions made by engineers with different expertise by learning the company-wide historical WBM classification results. Based on a real dataset with a total of 27,701 WBMs, our WBM classification model significantly outperformed benchmarked machine learning models. In addition, the visualization results of the proposed Bin2Vec method makes it easier to discover meaningful WBM patterns compared with the random RGB coloring scheme. We expect the proposed framework to improve both efficiencies by automating the bad wafer classification process and effectiveness by assigning similar bin codes and their corresponding colors on the WBM.

Graph Coloring Problems in Modern Computer Science

Graph coloring is one of the most important concepts in graph theory and is used in many real time applications in computer science. The main aim of this paper is to present the importance of graph coloring ideas in various areas of compute applications for researches that they can use graph coloring concepts for the research. Graph coloring used in various research areas of computer science such data mining, image segmentation, clustering, image capturing, networking etc. This papers mainly focused on important applications such as Guarding an Art Gallery, Physical layout segmentation, Round-Robin Sports Scheduling, Aircraft scheduling, Biprocessor tasks, Frequency assignment, Final Exam Timetabling as a Grouping Problem, Map coloring and GSM mobile phone networks, and Student Time Table. In this paper we review several variants of graph colouring, such as precolouring extension, list colouring, multicolouring, minimum sum colouring, and discuss their applications in scheduling. A very important graph parameter is the chromatic number. Presently, graph coloring plays an important role in several real-world applications and still engages exciting research.