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

  • 10Feb
  • 2015
  • 0
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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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