Page 77 - B.Tech IT Curriculum and Syllabus R2017 - REC

Department of IT, REC

SEMESTER VI
ELECTIVE - I

IT17E61 GRAPH THEORY AND APPLICATION L T P C
3 0 0 3
OBJECTIVES:
The student should be able to
 To develop an understanding the most fundamentals of Graphs, Sub graphs and Trees.
 To be familiar with the concept of Spanning trees, Cut sets, Isomorphism, Network flows and
Planar graphs.
 To learn about Directed graphs & its types, Euler graphs.

 To understand the principle of permutations and combinations.
 To learn about how to generate functions, solving homogeneous and non-homogeneous
recurrence relations.

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.
(Ref. Book 1: Chapter 1-3)

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 – Planar
graphs – Different representation of a planer graph.
(Ref. Book 1: Chapter 3-5)

UNIT III MATRICES, COLOURING AND DIRECTED GRAPH 9
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.
(Ref. Book 1: Chapter 8-9)

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.
(Ref. Book 2: Chapter 1 & 8)

UNIT V GENERATING FUNCTIONS 9
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
(Ref. Book 1: Chapter 9 & 10)
TOTAL: 45 PERIODS
OUTCOMES:
At the end the student will be able to
1. Write precise and accurate mathematical definitions of objects in graph theory.
2. Use mathematical definitions to identify and construct examples and to distinguish examples
from non-examples.

Curriculum and Syllabus | B.Tech. Information Technology | R2017 Page 77