Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

INSTITUTE OF SCIENCE / MAT605 - MATHEMATICS (DOCTORATE DEGREE)

Code: MAT605 Course Title: SPECTRAL GRAPH THEORY I Theoretical+Practice: 3+0 ECTS: 6
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) HATİCE TOPCU,
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course
To teach topics about spectral graph theory.

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 Can define various types of graph spectra. PO-3 Students will be dominated by current issues in mathematics.
 		Examination
LO-2 Can have knowledge about graph matrices and apply the topics of linear algebra. PO-2 Students will understand all aspects of mathematics and deepen the knowledge level that can innovate in this field.
 		Performance Project
LO-3 Can do spectral characterizations PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues.
 		Term Paper
Practice Exam
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Graph spectra, graph operations and modifications, Characterizations by spectra, Spectral characterizations of certain classes of graphs, The graph isomorphism problem
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Graph spectra Teaching topic and applications
2 Some results from linear algebra Teaching topic and applications
3 Graph operations and modifications Teaching topic and applications
4 Line graphs and related operations Teaching topic and applications
5 Spectra of graphs of particular types Teaching topic and applications
6 Counting certain subgraphs Teaching topic and applications
7 Connectedness and metric invariants Teaching topic and applications
8 mid-term exam
9 Regularrity and bipartiteness Teaching topic and applications
10 Spectral bounds for graph invariants Teaching topic and applications
11 Constraints on special eigenvalues Teaching topic and applications
12 Spectral characterizations of certain classes of graphs Teaching topic and applications
13 Cospectral graphs and the graph isomorphism problem Teaching topic and applications
14 Cospectral graphs and the graph isomorphism problem Teaching topic and applications
15 Characterizations by eigenvalues and angles Teaching topic and applications
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 Algebraic graph theory, U. Knauer, Studies in Math. 41, Berlin,2011
Required Course instruments and materials
The books of lecture

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