scholarly journals ANALISIS PENJADWALAN MATA PELAJARAN MENGGUNAKAN ALGORITMA WELCH-POWELL

2020 ◽  
Vol 3 (1) ◽  
pp. 1-21
Author(s):  
Pramitha Shafika Wicaksono ◽  
Kartono Kartono
Keyword(s):  
Graph Theory ◽  
Graph Coloring ◽  
Academic Staff ◽  
Vertex Coloring ◽  
The Subject ◽  
Coloring Graph

At the beginning of each semester, subjects scheduling is always carried out by the curriculum representatives and academic staff. There were several problems that must be avoided in subjects scheduling, these problems were the schedule of teachers who teach one subject at the same time are scheduled in different classes, teachers who teach more than one subject are scheduled in the same class at the same time, teachers who are lack of scheduled for teaching. In the subject of graph theory, there is a concept of graph coloring, one of which is vertex coloring. In vertex coloring, there is a Welch-Powell Algorithm application which produces a color for each vertex. In subject scheduling, it is assumed that the vertex is the subject and the teacher, while the edge is the class. In vertex coloring, graph vertices are colored so that there's no two neighboring vertices have the same color. The aim of this research was to arrange a lesson schedule so that problems do not occur such as clashes between teachers, subjects, and teaching hours. The method used in arranging this lesson schedule used the Welch-Powell Algorithm. The results obtained were using the Welch-Powell Algorithm to produce a lesson schedule every day where if there are two classes that have the same subject, they can meet the same day requirements but come in different hours and get a lesson schedule that has no clash between teachers, subjects, and teaching hours.

scholarly journals On Bi-gram Graph Attributes

2021 ◽  
Vol 14 (3) ◽  
pp. 78
Author(s):  
Thomas Konstantinovsky ◽  
Matan Mizrachi
Keyword(s):  
Graph Theory ◽  
Graph Coloring ◽  
Semantic Analysis ◽  
Large Datasets ◽  
Corpus Analysis ◽  
Graph Representation ◽  
New Approach ◽  
Graph Density ◽  
Coloring Graph ◽  
Basic Graph

We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a "bi-gram graph" representation of a corpus. The different attributes derived from graph theory are measured and analyzed as unique insights or against other corpus graphs, attributes such as the graph chromatic number and the graph coloring, graph density and graph K-core. We observe a vast domain of tools and algorithms that can be developed on top of the graph representation; creating such a graph proves to be computationally cheap, and much of the heavy lifting is achieved via basic graph calculations. Furthermore, we showcase the different use-cases for the bi-gram graphs and how scalable it proves to be when dealing with large datasets.

Fuzzy graph theory in coloring graph

2021 ◽  
Author(s):  
S. Sangeetha ◽  
P. Hema ◽  
N. Selvarani ◽  
P. Geetha ◽  
P. Karthikeyan ◽  
...  
Keyword(s):  
Graph Theory ◽  
Fuzzy Graph ◽  
Coloring Graph

scholarly journals Teaching Combinatorial Principles Using Relations through the Placemat Method

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1825
Author(s):  
Viliam Ďuriš ◽  
Gabriela Pavlovičová ◽  
Dalibor Gonda ◽  
Anna Tirpáková
Keyword(s):  
Graph Theory ◽  
Complexity Theory ◽  
Slovak Republic ◽  
Teaching Mathematics ◽  
Combinatorial Structures ◽  
Algorithmic Approach ◽  
Scientific Disciplines ◽  
Combinatorial Principles ◽  
The Subject ◽  
As Graph

The presented paper is devoted to an innovative way of teaching mathematics, specifically the subject combinatorics in high schools. This is because combinatorics is closely connected with the beginnings of informatics and several other scientific disciplines such as graph theory and complexity theory. It is important in solving many practical tasks that require the compilation of an object with certain properties, proves the existence or non-existence of some properties, or specifies the number of objects of certain properties. This paper examines the basic combinatorial structures and presents their use and learning using relations through the Placemat method in teaching process. The effectiveness of the presented innovative way of teaching combinatorics was also verified experimentally at a selected high school in the Slovak Republic. Our experiment has confirmed that teaching combinatorics through relationships among talented children in mathematics is more effective than teaching by a standard algorithmic approach.

scholarly journals Probability of an Intermediate (Reduced Operational) State

2021 ◽  
Vol 12 (3) ◽  
pp. 71-96
Author(s):  
Paweł SZCZEPAŃSKI
Keyword(s):  
Graph Theory ◽  
Intermediate State ◽  
Single Element ◽  
Additional Component ◽  
Kolmogorov Equations ◽  
The Subject ◽  
Basic Concepts ◽  
Operational Failure

This work examines with the form of the well-known sum: p + q = 1 – which is the sum of the probabilities of opposite events, in particular: the sum of the probabilities of the operational and non-operational (failure) states of a single element (a creation characterised by one output and any number of inputs). It was found that without significantly compromising the accuracy of the previous analyses, it was possible to introduce an additional component to the sum: iiipq3, a component that embodies the probability of an intermediate state, or a reduced operational state. With a constant value of the sum of the components in question, their variation as a function of probability q was determined, following which in the function of the same variable the variation of the entropy of an element's i state was examined using Chapman-Kolmogorov equations; here the focus was on investigating the intensity of the transition from the operational state to the non-operational state or an intermediate state, and from an intermediate state to the non-operational state. The meaning of intermediate probability was also referenced to the object: its diagnostic program, the entropy of structure, the full set of discriminable states, and the relevant transition intensities. It became indispensable in this respect to describe the object using the language of graph theory, in which the basic concepts are layers and an availability matrix. It should be noted that the subject object is an entity that comprises a set of individual elements, with a number and structure of connections that are consistent with the purpose of this entity.

scholarly journals A survey of graph coloring - its types, methods and applications

2012 ◽  
Vol 37 (3) ◽  
pp. 223-238 ◽  
Author(s):  
Piotr Formanowicz ◽  
Krzysztof Tanaś
Keyword(s):  
Graph Theory ◽  
Graph Coloring ◽  
Cubic Graphs ◽  
The World ◽  
Computer Scientists

Abstract Graph coloring is one of the best known, popular and extensively researched subject in the field of graph theory, having many applications and conjectures, which are still open and studied by various mathematicians and computer scientists along the world. In this paper we present a survey of graph coloring as an important subfield of graph theory, describing various methods of the coloring, and a list of problems and conjectures associated with them. Lastly, we turn our attention to cubic graphs, a class of graphs, which has been found to be very interesting to study and color. A brief review of graph coloring methods (in Polish) was given by Kubale in [32] and a more detailed one in a book by the same author. We extend this review and explore the field of graph coloring further, describing various results obtained by other authors and show some interesting applications of this field of graph theory.

An Algorithm for Testing Isomorphism of Planer Graph Based on Distant Matrix

2012 ◽  
Vol 487 ◽  
pp. 317-321
Author(s):  
Yan Peng Wu ◽  
Shui Qiang Liu
Keyword(s):  
Graph Theory ◽  
Polynomial Time ◽  
Time Complexity ◽  
Graph Isomorphism ◽  
Distance Matrix ◽  
Space Complexity ◽  
The Subject ◽  
The Many

The testing for graph isomorphism is one of the many problems in the subject of graph theory. This thesis proposes an algorithm for testing isomorphism of planer graph of polynomial time via structuring characteristics of planer graph based on distance matrix. The algorithm, with a time complexity of O (n^4) and a space complexity of O (n^2), has a great application value.

scholarly journals Kildekompasset - å navigere seg frem til riktig referansestil

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Hilde Daland ◽  
Birgitte Kleivset ◽  
Patricia Flor ◽  
Siv Holt
Keyword(s):  
Reference System ◽  
Response Rate ◽  
Academic Staff ◽  
Academic Library ◽  
Critical Evaluation ◽  
White Paper ◽  
Web Resource ◽  
The Subject ◽  
The University ◽  
Huge Challenge

One of the main tasks of an academic library is to guide students in critical evaluation and the ethical use of sources so that they can interpret, evaluate and create information in a correct and proper way. This should be integrated into the subjects, which is a huge challenge. Many students are told that they can freely select the reference style as long as they are consistent. But it is difficult to be consistent when you barely know what a reference style is. It is not easy for the librarian to answer how one refers to a governmental white paper in a self-designed reference system. To do this in a simple way, it is desirable to share the task between academic tutors and the library.  The recommendation of a reference style should come from the subject department of a faculty and from the sample collections provided by the library. The libraries at the University of Agder (UoA) and Telemark University College (TUC) joined forces to create a survey in which various reference styles were listed, complete with examples. The respondents were asked to choose the style they preferred  and would advise their students to use.  The response rate among the academic staff at the TUC and the UoA was 40%. We consider this to be a representative sample. The purpose of the final web resource aims to be as simple as possible. Students who do not know what a reference style is, and students who do not know which style they should choose, are now guided to make a confident choice of style.

scholarly journals Towards the co-identification of threshold concepts in academic reading

2020 ◽  
Vol 17 (2) ◽  
pp. 36-57
Author(s):  
Craig Morley ◽  
Keyword(s):  
Delphi Method ◽  
Teaching And Learning ◽  
Academic Staff ◽  
Threshold Concepts ◽  
Online Surveys ◽  
Academic Reading ◽  
The Subject ◽  
Study Participants ◽  
Potential Threshold

This paper seeks to identify threshold concepts in academic reading. It builds on existing research on the subject by working in collaboration with three groups of academic readers (1: academic staff and subject lecturers; 2: learning developers and librarians; 3: students) to co-identify a list of potential threshold concepts of academic reading. The Delphi Method was used to build a consensus between the different groups. Throughout the study, participants were invited to suggest and discuss threshold concepts across three rounds of asynchronous online surveys, which resulted in the identification of eight threshold concepts. It is hoped that these threshold concepts will enable and empower the teaching and learning of academic reading in a more transparent and explicit way.

Chromatic Zagreb and irregularity polynomials of graphs

2020 ◽  
pp. 2150061
Author(s):  
Smitha Rose ◽  
Sudev Naduvath
Keyword(s):  
Graph Coloring ◽  
Recent Literature ◽  
Structural Characteristics ◽  
Vertex Coloring ◽  
Proper Vertex

Graph coloring is an assignment of colors, labels or weights to elements of a graph subject to certain constraints. Coloring the vertices of a graph in such a way that adjacent vertices are having different colors is called proper vertex coloring. A proper vertex coloring using minimum parameters of colors is studied extensively in recent literature. In this paper, we define new coloring related polynomials, called chromatic Zagreb polynomials and chromatic irregularity polynomials, in terms of minimal parameter coloring and structural characteristics of graphs such as distances and degrees of vertices.

Graph Theory: A Look Back—The Road Ahead

2017 ◽  
Author(s):  
Arthur Benjamin ◽  
Gary Chartrand ◽  
Ping Zhang
Keyword(s):  
Social Networks ◽  
Graph Theory ◽  
The Internet ◽  
The Road ◽  
Eulerian Graphs ◽  
Bridge Problem ◽  
Look Back ◽  
Leonhard Euler ◽  
The Subject ◽  
The 1960S

This book concludes with an epilogue, which traces the evolution of graph theory, from the conceptualization of the Königsberg Bridge Problem and its generalization by Leonhard Euler, whose solution led to the subject of Eulerian graphs, to the various efforts to solve the Four Color Problem. It considers elements of graph theory found in games and puzzles of the past, and the famous mathematicians involved including Sir William Rowan Hamilton and William Tutte. It also discusses the remarkable increase since the 1960s in the number of mathematicians worldwide devoted to graph theory, along with research journals, books, and monographs that have graph theory as a subject. Finally, it looks at the growth in applications of graph theory dealing with communication and social networks and the Internet in the digital age and the age of technology.

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