Graph Theory (All Units) Premium Lecture Notes - Anitha Edition

Graph Theory Premium (All Units) Handwritten Premium Lecture Notes, Prepared by Anitha. Specially for M.Sc Candidates. Syllabus Covered based on University of Madras , M.Sc First Semester.

Syllabus :

UNIT-1 (pg.no 1-30) : GRAPH AND SIMPLE GRAPH
UNIT-2 (pg.no 32-54) : CONNECTIVITY OR VERTEX CONNECTIVITY
UNIT-3 (pg.no 55-72) : MATCHINGS
UNIT-4 (pg.no 74-99)  : INDEPENDENT SETS AND CLIQUES
UNIT-5 (pg.no 100-112) : PLANE AND PLANER GRAPH

Content :

UNIT-1
GRAPH AND SIMPLE GRAPH
Planar graph
Graph isomorphism
Complete graph
The incidence and adjacency matrices
Sub graph
Vertex degrees
Degree-sum formula
Wrollery
Cycles
Characterization of bipartite graph
Tress
Corollary
Cut edges and bonds
Spanning tree
Cut-vertices

UNIT-2
CONNECTIVITY OR VERTEX CONNECTIVITY
Blocks
Subdivision of an edges
Euler tour andhamilton cycles
Hamiltonian cycles
Lemma

UNIT-3
MATCHINGS
Matching
Neighbor sets
Matching and converings in sipartite graph
Suf part
The marriage problems
Lemma (konig’s lemma)
Edge colourings
Two elementary properties

UNIT-4
INDEPENDENT SETS AND CLIQUES
Independent sets
Gallai
Ramsey’s theory
Ramsey numbers
Erdos
Vertex colouring
Chromatic number
Illustration of S-components of grsph G
Brook’s theorem
Chromatic polynomials

UNIT-5
PLANE AND PLANER GRAPH
Dual graph
Eulers formula