Graph Theory | by Udit Agarwal and Umesh Pal Singh | ISBN: 9788131807743. Computer Science Books. Euler and Hamiltonian Graphs. Vector Space Associated with a Graph. Detection of Planarity of a Graph. Ford and Fulkerson Algorithm

Graph Theory
by Udit Agarwal and Umesh Pal Singh
ISBN:9788131807743
Written in a reader-friendly style with features that enhance students’ comprehension, this concise book explains the principles and fundamental concepts of graph theory.




Graph Theory
Preface
Chapter 1 – Elementary Combinatorics
1.1: Introduction
1.2: Basic Counting Principles
1.3: The Inclusion – Exclusion Principle
1.4: Permutations (Arrangement of Objects)
1.5: Combinations
1.6: Probability
Exercises

Chapter 2 – Discrete Numeric Functions and Generating Functions
2.1: Discrete Numeric Functions
2.2: Manipulation of Numeric Functions
2.3: Definitions of Si a and S-i a for a Numeric Function
2.4: Generating Function
2.5: Operations on Generating Functions
2.6: Finding a Generating Function of the Fibonacci Sequence
2.7: Solution of Combinatorial Problems Using Generating Functions
Exercises

Chapter 3 – Recurrence Relations
3.1: Introduction
3.2: Order of Recurrence Relation
3.3: Degree of the Recurrence Relation
3.4: Solution of Linear Recurrence Relation with Constant Co-Efficients
3.5: Solution of Recurrence Relation by the Method of Generating Function
3.6: Backtracking Method
3.7: Forward Chaining Method
3.8: Summation Method
Exercises

Chapter 4 – Graphs
4.1: Introduction
4.2: What is a Graph ?
4.3: Basic Terminologies
4.4: Regular Graph
4.5: Complete Graph
4.6: Null Graph
4.7: Bipartite Graph
4.8: Degree Sequence
4.9: Graphs Isomorphism
4.10: Complement of a Simple Graph
4.11: Homeomorphic Graphs
4.12: Subgraphs
4.13: Operations of Graphs
4.14: Connected Graphs and Disconnected Graphs
4.15: Walk, Paths and Circuits
Exercises

Chapter 5 – Euler and Hamiltonian Graphs
5.1: Euler Graphs
5.2: Unicursal Graph
5.3: Constructing Eulerian Paths and Cycles
5.4: Hamiltonian Graphs
5.5: Introduction to Travelling Salesman Problem
5.6: Chinese Postman Problem
Exercises




Chapter 6 – Trees
6.1: Introduction
6.2: Trivial and Non-trivial Tree
6.3: Properties of Trees
6.4: Rooted Trees
6.5: Pendant Vertex
6.6: Distance and Centers in a Tree
6.7: Binary Trees
6.8: Counting Tree
6.9: Spanning Tree
6.10: Shortest Path Problems
6.11: Fundamental Circuits
Exercises

Chapter 7 – Cut-sets and Net Work Flows
7.1: Cut-sets
7.2: Fundamental Cut-Set
7.3: Connectivity
7.4: Separable Graph
7.5: Network-Flow Problems (Transport Network)
7.6: Ford and Fulkerson Algorithm
7.7: Cut and Its Capacity
7.8: Max-Flow Min-Cut Theorem
Exercises

Chapter 8 – Planar and Dual Graphs
8.1: Introduction
8.2: Kuratowski’s Graphs
8.3: Region
8.4: Euler’s Formula
8.5: Some Planar Graphs
8.6: Detection of Planarity of a Graph
8.7: Geometric Dual
8.8: Combinatorial Dual
8.9: Thickness and Crossing
Exercises

Chapter 9 – Vector Spaces of a Graph
9.1: Introduction
9.2: Sets with One Operation
9.3: Modular Arithmetic
9.4: Galois Fields
9.5: Vectors
9.6: Vector Space
9.7: Vector Space Associated with a Graph
9.8: Basis Vectors of a Graph
9.9: Circuit and Cut-set Subspaces
9.10: Orthogonal Vectors and Spaces
Exercises

Chapter 10 – Matrix-Representation of Graphs
10.1: Introduction
10.2: Incidence Matrix
10.3: Circuit Matrix
10.4: Cut-set Matrix
10.5: Relationship between AF, BF and CF
10.6: Path Matrix
10.7: Adjacency Matrix
Exercises

Chapter 11 – Coloring of Graphs
11.1: Graph Coloring
11.2: Chromatic Number
11.3: Chromatic Partitioning and Independent Sets
11.4: Chromatic Polynomial
11.5: Matching
11.6: Covering
11.7: Four Color Problem
11.8: The Five Color Theorem
11.9: The Six Color Theorem
Exercises

Chapter 12 – Directed Graphs
12.1: Introduction
12.2: Directed Graph
12.3: Types of Digraphs
12.4: Directed Paths and Connectedness
12.5: Binary Relations and Directed Graphs
12.6: Euler Directed Graphs
12.7: Trees with Directed Edges
12.8: Arborescence
12.9: Acyclic Digraphs
12.10: Fundamental Circuit in Directed Graphs
12.11: Incidence Matrix of a Digraph
12.12: Circuit Matrix of a Digraph
12.13: Adjacency Matrix of a Digraph
12.14: Orientations and Tournaments
Exercises

Chapter 13 – Enumeration of Graphs
13.1: Types of Enumeration
13.2: Cayley’s Theorem
13.3: Counting Unlabeled Trees
13.4: Rooted Unlabeled Trees
13.5: Free Unlabeled Trees
13.6: Permutation
13.7: Polya’s Counting Theorem
13.8: Graph Enumeration with Polya’s Theorem
Exercises

Chapter 14 – Applications of Graph Theory
14.1: Introduction
14.2: Graphs in Computer Science
14.3: Miscellaneous Applications
Exercises

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