MCF1D Graph Theory Scanned Lecture Notes (All Units) - Anitha Edition

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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

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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

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