Information Package / Course Catalogue
Graph Theory and Applications in Mathematics Education
Course Code: MTE534
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

To give students the opportunity to construct the basics and concepts of graph theory and develop their perspectives.

Course Content

History of graph theory and some usage areas, definition of graph, types of graphs and matrix representations of graphs, connectivity and isomorphic graphs, operations in graphs, Euler and Hamilton graphs, planar and non-planar graphs, coloring in graphs and type of graph. The place of graph theory in mathematics education and examination of studies in the literature.

Name of Lecturer(s)
Learning Outcomes
1.Learns the history of graph theory.
2.Understands and explains the basic concepts of graph theory.
3.Can explain Euler and Hamilton diagrams by giving examples from daily life.
4.Understands what coloring is.
5.Solves problems that require the application of graph theory.
Recommended or Required Reading
1.J. Trudeau, Introduction to Graph Theory, Dover Publication, 1993.
2.J. Clark, D. A. Holton, A First Look At Graph Theory, World Scientific, 1991.
3.Tutte, W. T., & Tutte, W. T. (2001). Graph theory (Vol. 21). Cambridge university press.
Weekly Detailed Course Contents
Week 1 - Theoretical
History of graph theory and some applications.
Week 2 - Theoretical
Basic concepts in graph theory
Week 3 - Theoretical
Graph types and Matrix representation
Week 4 - Theoretical
Connectivity and isomorphic graphs
Week 5 - Theoretical
Graph operations and the concept of distance in graphs
Week 6 - Theoretical
Eulerian and Hamiltonian graphs
Week 7 - Theoretical
Application of graphs to daily life problems
Week 8 - Theoretical
Shortest path problem. (Midterm Exam)
Week 9 - Theoretical
Planar graphs and Euler's formula
Week 10 - Theoretical
Kind of a graph and non-planar graphs
Week 11 - Theoretical
Coloring problem
Week 12 - Theoretical
The place of graph theory in mathematics education
Week 13 - Theoretical
Relationship of graph theory with other disciplines (Engineering, software, number theory)
Week 14 - Theoretical
Examination of graph theory studies in mathematics education national and international literature
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%30
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory142370
Midterm Examination128230
Final Examination148250
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
OÇ-1
3
4
5
1
4
4
4
4
3
3
OÇ-2
3
3
4
2
3
3
3
3
4
2
OÇ-3
4
4
4
3
4
4
4
4
4
3
OÇ-4
1
3
3
2
3
2
4
2
3
1
OÇ-5
2
3
5
3
3
2
5
1
4
2
Adnan Menderes University - Information Package / Course Catalogue
2026