Introduction

The Konigsberg Bridge problem

Four color problem

Team competitions

Graph Theory today

Graphs and Subgraphs

Introduction

Definition and examples

Degrees

Subgraphs

Isomorphism

Ramsey numbers

Independent sets and coverings

Intersection graphs and line graphs

Matrices associated with a graph

Operations on graphs

Degree Sequences

Introduction

Degree sequences

Graphic sequences

Connectedness

Introduction

Walks, trails and paths

Connectedness and components

Blocks

Connectivity

Eulerian and Hamiltonian Graphs

Introduction

Eulerian graphs

Hamiltonian graphs

Trees

Introduction

Characterisation of trees

Centre of a tree

Matchings

Introduction

Matchings

Matchings in bipartite graphs

Planarity

Introduction

Definition and properties

Characterization of planar graphs

Thickness, crossing and outer planarity

Graph Colorings

Introduction

Chromatic number and chromatic index

The five color theorem

Four color problem

Chromatic polynomials

Domination in Graphs

Introduction

Domination number of a graph

Bounds on the domination number

Independent, connected and total domination in graphs

Graph Labelings

Introduction

Graceful labeling

Magic and antimagic edge labelings

Distance magic graphs

Directed Graphs

Introduction

Definitions and basic properties

Paths and connections

Digraphs and matrices

Tournaments

Some Applications

Introduction

Connector problem

Shortest path problem

Transformation and Kinematic graph

Designing one way traffic systems

Applications without efficient solutions

Some Research Areas

Introduction

Reconstruction conjecture

Domination in graphs

Graph labeling problems

Algebraic graph theory

Hamiltonian graphs

Ramsey numbers

Edited volumes

Index

Dr. S. Arumugam is an eminent mathematician currently serving as Honorary Professor of Eminence at Ramanujan College, New Delhi. He previously held distinguished academic positions including Professor of Mathematics at St. John’s College, Palayamkottai (1968–1992), Founder Professor and Head of the Department of Mathematics at Manonmaniam Sundaranar University, Tirunelveli (1992–2003), and Senior Professor (Research) and Director of the National Centre for Advanced Research in Discrete Mathematics at Kalasalingam Academy of Research and Education (2003–2017). .

 Dr. S. Ramachandran earned his M.Sc. from Madurai Kamaraj University and began his academic career at Aditanar College of Arts and Science, Tiruchendur, in 1970. He pursued research at the Ramanujan Institute for Advanced Study in Mathematics, University of Madras (1975–76), and at the School of Mathematics, Madurai Kamaraj University (1977–80), completing his Ph.D. in 1982 on Ulam’s Conjecture in Graph Theory. A dedicated researcher, he has published around 40 papers in Graph Theory, reviewed articles for reputed journals, and guided scholars at the doctoral level.