CS6702 GRAPH THEORY AND APPLICATIONS | syllabus

CS6702 GRAPH THEORY AND APPLICATIONS L T P C 3 0 0 3

OBJECTIVES:

The student should be made to:
 Be familiar with the most fundamental Graph Theory topics and results.
 Be exposed to the techniques of proofs and analysis.

UNIT I      INTRODUCTION    (9)

Graphs – Introduction – Isomorphism – Sub graphs – Walks, Paths, Circuits –Connectedness –
Components – Euler graphs – Hamiltonian paths and circuits – Trees – Properties of trees – Distance
and centers in tree – Rooted and binary trees.

UNIT II      TREES, CONNECTIVITY & PLANARITY    (9)

Spanning trees – Fundamental circuits – Spanning trees in a weighted graph – cut sets – Properties
of cut set – All cut sets – Fundamental circuits and cut sets – Connectivity and separability – Network
flows – 1-Isomorphism – 2-Isomorphism – Combinational and geometric graphs – Planer graphs –
Different representation of a planer graph.

UNIT III      MATRICES, COLOURING AND DIRECTED GRAPH    (8)

Chromatic number – Chromatic partitioning – Chromatic polynomial – Matching – Covering – Four
color problem – Directed graphs – Types of directed graphs – Digraphs and binary relations –
Directed paths and connectedness – Euler graphs.

UNIT IV      PERMUTATIONS & COMBINATIONS    (9)

Fundamental principles of counting - Permutations and combinations - Binomial theorem -
combinations with repetition - Combinatorial numbers - Principle of inclusion and exclusion -
Derangements - Arrangements with forbidden positions.

UNIT V      GENERATING FUNCTIONS    (10)

Generating functions - Partitions of integers - Exponential generating function – Summation operator -
Recurrence relations - First order and second order – Non-homogeneous recurrence relations -
Method of generating functions.

                                                                                                                         TOTAL: 45 PERIODS

OUTCOMES:

Upon Completion of the course, the students should be able to:
 Write precise and accurate mathematical definitions of objects in graph theory.
 Use mathematical definitions to identify and construct examples and to distinguish examples
from non-examples.
 Validate and critically assess a mathematical proof.
 Use a combination of theoretical knowledge and independent mathematical thinking in creative
investigation of questions in graph theory.
 Reason from definitions to construct mathematical proofs.

TEXT BOOKS:

1. Narsingh Deo, “Graph Theory: With Application to Engineering and Computer Science”,
Prentice Hall of India, 2003.
2. Grimaldi R.P. “Discrete and Combinatorial Mathematics: An Applied Introduction”, Addison
Wesley, 1994.

REFERENCES:

1. Clark J. and Holton D.A, “A First Look at Graph Theory”, Allied Publishers, 1995.
2. Mott J.L., Kandel A. and Baker T.P. “Discrete Mathematics for Computer Scientists and
Mathematicians” , Prentice Hall of India, 1996.
3. Liu C.L., “Elements of Discrete Mathematics”, Mc Graw Hill, 1985.
4. Rosen K.H., “Discrete Mathematics and Its Applications”, Mc Graw Hill, 2007

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