MSc (Mathematics and Computing) Programme:Graph Theory and Applications

Semester I

Real Analysis – I
Linear Algebra
Complex Analysis
Fundamentals of Computer Science and C Programming
Discrete Mathematical Structure
Differential Equations


Semester II

Real Analysis –II
Advanced Abstract Algebra
Computer Oriented Numerical Methods
Data Structures
Data Based Management Systems
Operating Systems


Semester III

Topology
Computer Based Optimization Techniques
Computer Networks
Mechanics
Seminar


Semester IV

Functional Analysis
Dissertation


Graph Theory and Applications

Graphs and Subgraphs: Graph and Simple Graphs, Graph Isomorphism, Incidence and adjacency matrix, subgraphs, Vertex, Degrees, Paths and connection, Cycles, directed graphs, directed paths, directed cycles, The shortest path problems, Sperner’s lemma, A job sequencing problems, Designing an efficient computer Drum, Making a Road system One-way, Ranking the participants in a tournament

Trees and Networks: Trees, Cut edges and bonds, Cut vertices, Cayley Formula, Flows, Cuts, The max-Flow Min- Cut theorem, Connectivity, Blocks. The Connector problem, Menger’s theorem, Feasible Flows, Construction of Reliable Communication Networks

Planar Graphs: Plane and planar Graphs, Dual graphs, Euler’s formula, Bridges, Kuratowski’s theorem, The five - colour theorem and the four-colour conjecture, non- Hamiltonian planar Graphs. A planarity Algorithm.

Euler's Tours and Hamilton's Cycls: Euler’s tours, Hamilton cycles, The Chinese postman problem, the traveling salesman problem, Industrial drilling tool problem.

Matching: Matching in Bipartite graphs, perfect matching. The personnel Assignment problems, The optimal assignment problems.

Colorings: Edge chromatic number, Vizing’s theorem, Brook’s theorem, Hajos’s conjecture, Chromatic polynomials, Girith and Chromatic number. The time tabling problems, Storage problem.

Laboratory work: The laboratory work shall be based upon the implementation of graph theory algorithms like paths, circuits, shortest path problems, tree, Euler’s tour,Hamilton cycles, Chinese postman problem, the traveling salesman problem, Matching in Bipartite graphs, coloring of graphs through a suitable language such as C/C++.