Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Fall Semester | ||||
| Level of Course | 3rd Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | MATHEMATICS (DOCTORATE DEGREE) | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | SEZER SORGUN (ssorgun@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | |||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| To understand the issues related to energy by introducing Graf spectras, | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Introductionto Graph Energy and other mathematical connections, Characteristic Polynomial of a Graph, Back to Total pi-Electron Energy, Huckel Molecular Orbital Theory, The Coulson Integral Formula, Graphs Extremal with Regard to Energy, Hyperenergeticand Equienergetic Graphs | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Introduction to Graph Energy | Teaching |
| 2 | Characteristic Polynomial of Graphs | Teaching |
| 3 | Huckel Molecular Orbital Theory | Teaching |
| 4 | The Coulson Integral Formula | Teaching |
| 5 | Spectral Moments | Teaching |
| 6 | Graph Operations | Teaching |
| 7 | Upper Bounds for General Graphs | Teaching |
| 8 | mid-term exam | |
| 9 | Upper Bounds for Bipartite Graphs | Teaching |
| 10 | Upper Bounds for Regular Graphs | Teaching |
| 11 | The Energy of Random Bipartite Graphs | Teaching |
| 12 | The Energy of Random Bipartite Graphs | Teaching |
| 13 | Maximal Energy of Trees with Given MaximumDegree | Teaching |
| 14 | Maximal Energy of Trees with Given MaximumDegree | Teaching |
| 15 | Minimal Energyof Unicyclic Graphs. | Teaching |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | An introduction to the theory of Graph Spectra, D.Cvetkovic,P.Rowlinson and S.Simic, London Mathematical Society Student Text 75, Cambridge Uni.Press,2010. | |
| 2 | Graph energy, X.Li,Y.,Shi, I.Gutman, Springer,2012. | |
| Required Course instruments and materials | ||
| Lecture books | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 2 | 30 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | 7 | 2 | 10 |
| 8.Term Paper | 14 | 2 | 10 |
| 9.Project | |||
| final exam | 16 | 2 | 50 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 3 | 14 | 42 |
| Outside Class | |||
| a) Reading | 2 | 14 | 28 |
| b) Search in internet/Library | 2 | 14 | 28 |
| c) Performance Project | 3 | 7 | 21 |
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 3 | 7 | 21 |
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 3 | 8 | 24 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 3 | 8 | 24 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 192 | ||