# Graph Theory and Applications

 Course Code : ULZ0200 Author : uLektz University : General for All University Regulation : 2017 Categories : Computer Science Format : ePUB3 (DRM Protected) Type : eBook

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Description :Graph Theory and Applications of ULZ0200 covers the latest syllabus prescribed by General for All University for regulation 2017. Author: uLektz, Published by uLektz Learning Solutions Private Limited.

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

##### Topics
###### UNIT I INTRODUCTION

1.1 Graphs - Introduction

1.2 Isomorphism

1.3 Sub graphs - Walks, Paths, Circuits

1.4 Connectedness

1.5 Components

1.6 Euler graphs

1.7 Hamiltonian paths and circuits

1.8 Trees - Properties of trees - Distance and centers in tree - Rooted and binary trees

###### UNIT II TREES, CONNECTIVITY & PLANARITY

2.1 Spanning trees

2.2 Fundamental circuits

2.3 Spanning trees in a weighted graph

2.4 Cut sets - Properties of cut set - All cut sets - Fundamental circuits and cut sets

2.5 Connectivity and separability

2.6 Network flows

2.7 1-Isomorphism

2.8 2-Isomorphism

2.9 Combinational and geometric graphs

2.10 Planer graphs - Different representation of a planer graph.

###### UNIT III MATRICES, COLOURING AND DIRECTED GRAPH

3.1 Chromatic number

3.2 Chromatic partitioning

3.3 Chromatic polynomial

3.4 Matching

3.5 Covering

3.6 Four color problem

3.7 Directed graphs - Types of directed graphs

3.8 Digraphs and binary relations

3.9 Directed paths and connectedness

3.10 Euler graphs.

###### UNIT IV PERMUTATIONS & COMBINATIONS

4.1 Fundamental principles of counting

4.2 Permutations and combinations

4.3 Binomial theorem

4.4 Combinations with repetition

4.5 Combinatorial numbers

4.6 Principle of inclusion and exclusion

4.7 Derangements

4.8 Arrangements with forbidden positions.

###### UNIT V GENERATING FUNCTIONS

5.1 Generating functions

5.2 Partitions of integers

5.3 Exponential generating function

5.4 Summation operator

5.5 Recurrence relations

5.6 First order and second order

5.7 Non-homogeneous recurrence relations

5.8 Method of generating functions.