Simple Graphs – Graph Isomorphism – The Incidence and Adjacency matrices – Sub graphs – Vertex Degrees – paths and Connection – Cycles, Trees – Cut edges and Bonds – cut vertices – Cayley‘s formula
Blocks, Euler tours and Hamilton Cycles.
Matchings, coverings in Bipartite Graphs – Perfect Matchings. Edge colourings: Edge chromatic number.
Independent sets – Ramsey‘s theorem. Vertex Colourings: Chromatic Number – Brook‘s Theorem – Hajos Conjecture – Chromatic Polynomials – Girth and Chromatic number.
Plane and planar Graphs – Dual Graphs – Euler‘s formula. The Five Colour Theorem and the Four Colour Conjecture – Non-Hamiltonian planar Graphs. Directed Graphs – Directed paths - Directed cycles
Reference Book:
Graph Theory with Applications by J.A. Bondy and U.S.R. Murty, American Elsevier Publishing Company, Inc., New York, 1976.
Text Book:
Graph Theory with Applications by J.A. Bondy and U.S.R. Murty, American Elsevier Publishing Company, Inc., New York, 1976.