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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS CSC 5031 GRAPH THEORY TECHNIQUES IN MATHEMATICAL MODELLING ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Third Cycle Programmes (Doctorate Degree)

Course Coordinator

ASSOCIATE PROFESSOR FIDAN NURIYEVA

Offered to

Ph.D. in Computer Science (English) Computer Science

Course Objective

The aim of this course is to introduce to students the extremal problems and special graphs.

Learning Outcomes of the Course Unit

1   Modeling real world problems with linear programming and graph. 2   Solving these problems with graph.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 The relation between graphs and computer science. Basic definitions 2 Constructing graphs. Havel-Hakim Theorem, complement of a graph, regular graphs, star graph, (Complete) Bipartite graphs, induced subgraphs, isomorphic graphs 3 Connectivity of graphs and some theorems. Graph operations (union, sum and product). Definition of trees and some theorems. Average degree of graphs, spanning subgraphs, wheel graph. 4 The definition of coloring, critic graphs, theorems on coloring, solution of a real-world problem with coloring, edge-coloring 5 Contraction, chromatic polynomials, chromatic polynomial and spanning subtree number finding algorithms with contraction 6 Königsberg Bridge Problem, theorems and definitions related KBP 7 Representing graphs on computer. Vertex-vertex and vertex-edge adjacency matrices. The properties of these matrices and theorems on it. 8 Recap 9 The shortest spanning tree of a graph 10 Steiner problem 11 Linear programming model of shortest path problem 12 The shortest paths between all pairs of vertices and algorithms 13 The shortest problem two specified vertices and algorithms 14 Matching and solution algorithms

Recomended or Required Reading

Textbook(s): 1. Chiristofides, N., Graph Theory An Algorithmic Approach , Academic Press, London,(1975). Supplementary Book(s): 1. Taha, H., Operation Research , Printice Hall, Fayetville, (1995)

Planned Learning Activities and Teaching Methods

The course is taught in a lecture, class presentation and discussion format. Besides the taught lecture, group presentations are to be prepared by the groups assigned and presented in a discussion session. In some weeks of the course, results of the homework given previously are discussed.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 MTE MIDTERM EXAM 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

fidan.nuriyeva@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 3 42 Preparation for midterm exam 1 20 20 Preparation for final exam 1 20 20 Preparing assignments 2 20 40 Preparing presentations 2 15 30 Preparations before/after weekly lectures 13 4 52 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 208

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 LO.1 5 5 5 5 LO.2 5 5 5 5