| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT4057 | Graph Theory | Fall | 3 | 0 | 3 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor MOHAMED KHALIFA |
| 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. |
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The students who have succeeded in this course; The students who succeeded in this course; o will be able to define and analyze problems and to find solutions based on scientific methods. o will be able to understand basic concepts of graph theory o will be able to apply the graph coloring methods to the daily life problems o will be able to use the dynamic graphs for helath sciences |
| Graphs, some special graphs, connectivity, blocks, trees, linear paths, planarity, Kuratowsky theorem, coloring, cromatic numbers, five color theorem, four color theorem, petri nets. |
| Week | Subject | Related Preparation | |
| 1) | Graph | ||
| 2) | Specific Graphs | ||
| 3) | Graph modelling and applications. | ||
| 4) | Walk, Distance, Path, Cycle and Trees | ||
| 5) | Subgraph and graph operations | ||
| 6) | Graph Isomoprhism | ||
| 7) | Trees: Binary Trees | ||
| 8) | Catalan Numbers. Travelling Binary Trees. Spanning Trees. | ||
| 9) | Edge and Vertex Connectivity. | ||
| 10) | Network Reliability. | ||
| 11) | MaxMin Duality and Menger’s Theorem. Eular Path | ||
| 12) | Hamilton Paths and Cycles. Travelling Sales Man Problem | ||
| 13) | Binary operations and Graphs. | ||
| 14) | Graph coloring and applications in mathematica. Petri nets. | ||
| Course Notes: | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | 2 | % 5 |
| Homework Assignments | 7 | % 5 |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 50 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 40 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 0 | 0 | 0 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 7 | 4 | 28 |
| Quizzes | 2 | 5 | 10 |
| Preliminary Jury | 0 | ||
| Midterms | 2 | 10 | 20 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 25 | 25 |
| Total Workload | 125 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |