Weeks | Topics |
1 |
The concept of graph and importance of graph theory.
|
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.
|
4 |
The process of coloring. Vertex color. Edge color. Some theorems of coloring. solution of a some problems with coloring.
|
5 |
Contraction, chromatic polynomials, chromatic polynomial and spanning subtree number finding algorithms with contraction.
|
6 |
Representing graphs on computer. Vertex-vertex and vertex-edge adjacency matrices. The properties of these matrices and theorems on it.
|
7 |
Vertex-cut, Vertex-cut matrices, basic vertex-cut and its matrix .
|
8 |
Matching. Maximal matching, perfect matching, (augmenting path), assignment problem, the modeling of assignment problem with graphs and Hungarian algorithm.
|
9 |
Connectivity number and Algorithms.
|
10 |
Distance in Graphs and Algorithms.
|
11 |
Graph Algorithms and Analysis
|
12 |
Graph Algorithms and Analysis
|
13 |
Modelling communication networks and Vulnerability
|
14 |
Modelling communication networks and Vulnerability
|