COURSE INTRODUCTION AND APPLICATION INFORMATION

Course Name
Graph Theory
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 659
Fall/Spring
3
0
3
7.5
Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
Third Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s) -
Course Objectives Definition of Disconnected structures and their applications. The aim gives the application of graph theory in computer sciences, operation research, social sciences and biomathematics. In this concept connectivity, graph coloring, trees, Euler and Hamilton paths, Cycles, Mathcing, Covering, Shortest path and network structures will be given.
Learning Outcomes The students who succeeded in this course;
  • will be able to define and analyze problems and to find solutions based on scientific methods.
  • will be able to understand basic concepts of graph theory
  • will be able to apply the graph coloring methods to the daily life problems
  • will be able to use the dynamic graphs for helath sciences
Course Description Graphs, some special graphs, connectivity, blocks, trees, linear paths, planarity, Kuratowsky theorem, coloring, cromatic numbers, five color theorem, four color theorem, petri nets.
Related Sustainable Development Goals

 



Course Category

 Core Courses
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Graph R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
2 Specific Graphs R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
3 Graph modelling and applications. R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
4 Walk, Distance, Path, Cycle and Trees R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
5 Subgraph and graph operations R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
6 Midterm
7 Graph Isomoprhism R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
8 Trees: Binary Trees R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
9 Catalan Numbers. Travelling Binary Trees. Spanning Trees. R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
10 Edge and Vertex Connectivity. Network Reliability. R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
11 MaxMin Duality and Menger’s Theorem.  Eular Path R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
12 Hamilton Paths and Cycles. Travelling Sales Man Problem R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
13 Binary operations and Graphs. R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
14 Graph coloring and applications in mathematica. R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
15 Petri Nets R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
16 Review of the Semester  
Course Notes/Textbooks J.Gross & J.Yellen, Graph Theory and its Applications, CRC Press, 1998
Suggested Readings/Materials Graph Theory: Modeling, Applications, and Algorithms, by Geir Agnarsson and Raymond Greenlaw, Pearson Prentice Hall, 2007

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
1
5
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
2
20
Project
1
25
Seminar / Workshop
Oral Exam
Midterm
1
20
Final Exam
1
30
Total

Weighting of Semester Activities on the Final Grade
70
Weighting of End-of-Semester Activities on the Final Grade
30
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
10
8
80
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
2
10
Project
1
7
Seminar / Workshop
Oral Exam
Midterms
1
30
Final Exams
1
40
    Total
225

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
 Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To have an appropriate knowledge of methodological and practical elements of the basic sciences and to be able to apply this knowledge in order to describe engineering-related problems in the context of industrial systems.
2

To be able to identify, formulate and solve Industrial Engineering-related problems by using state-of-the-art methods, techniques and equipment.
3

To be able to use techniques and tools for analyzing and designing industrial systems with a commitment to quality.
4

To be able to conduct basic research and write and publish articles in related conferences and journals.
5

To be able to carry out tests to measure the performance of industrial systems, analyze and interpret the subsequent results.
6

To be able to manage decision-making processes in industrial systems.
7

To have an aptitude for life-long learning; to be aware of new and upcoming applications in the field and to be able to learn them whenever necessary.
8

To have the scientific and ethical values within the society in the collection, interpretation, dissemination, containment and use of the necessary technologies related to Industrial Engineering.
9

To be able to design and implement studies based on theory, experiments and modeling; to be able to analyze and resolve the complex problems that arise in this process; to be able to prepare an original thesis that comply with Industrial Engineering criteria.
10

To be able to follow information about Industrial Engineering in a foreign language; to be able to present the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest