CS6702 GRAPH THEORY AND APPLICATIONS syllabus-subject-notes-pevious-year-questions-papers-bank
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.
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.
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.
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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