CIA 1 (A)

GRAPH THEORY

Submitted By - SAGAR

4 BCA - B

22215149

4 BCA - B

22215149

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Table of ContentsLoading...

Page 04 - 05 Aknowledgement and Preface....

Page 08 - 09 Introduction and What is Connectivity....

Page 10 - 11 Examples of Connected And Disconnected Graph...

Page 12 - 13 Common Questions Related to Graph theory...

Page 14 - 15 Levels of Connectivity And Video...

Page 16 Edge Connectivity...

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AKNOWLEDGEMENT

I would like to express my deepest gratitude to everyone who contributed to the realization of this book, "Graphs Theroy Basics." Writing a book and I am fortunate to have received support and encouragement from various individuals.

I extend my heartfelt thanks to

I extend my heartfelt thanks to

**Marlin Mam**for her invaluable guidance and mentorship throughout the writing process. Her expertise and enthusiasm for the subject matter greatly enriched the content of this book. I am truly grateful for the time, knowledge, and encouragement she generously shared.PREFACE

This book is an invitation to step into that world, to navigate the labyrinthine alleys of graphs and witness the beauty of their structure. We will traverse paths less traveled, from the foundational basics of connectivity and paths to the breathtaking heights of spectral analysis and extremal configurations. Along the way, we will encounter bridges constructed with logic, tunnels dug with algorithms, and landscapes painted by powerful theorems.

This journey is not merely an academic pursuit; it is a practical toolkit for unlocking the secrets of our interconnected world. Whether you are a budding engineer seeking to optimize communication networks, a scientist unraveling the intricate dance of molecules, or simply a curious mind yearning to understand the hidden patterns that bind us, graph theory has something to offer.

This journey is not merely an academic pursuit; it is a practical toolkit for unlocking the secrets of our interconnected world. Whether you are a budding engineer seeking to optimize communication networks, a scientist unraveling the intricate dance of molecules, or simply a curious mind yearning to understand the hidden patterns that bind us, graph theory has something to offer.

Connectivity

Graph theory finds applications in diverse fields like social network analysis, traffic optimization, bioinformatics, and computer science, constantly expanding its reach and relevance.

INTRODUCTION

**In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs.[1] It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network.**

In an undirected

**graph G**, two

**vertices u**and

**v**are called connected if

**G**contains a path from

**u**to

**v**. Otherwise, they are called disconnected. If the two vertices are additionally connected by a path of length 1 (that is, they are the endpoints of a single edge), the vertices are called

**adjacent.**

A

**directed graph**is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph. It is unilaterally connected or unilateral (also called semiconnected) if it contains a directed path from

**u**to

**v**or a directed path from

**v**to

**u**for every pair of

**vertices u, v**.[2] It is strongly connected, or simply strong, if it contains a directed path from

**u**to

**v**and a directed path from

**v**to

**u**for every pair of v

**ertices u, v.**

**CAPTION**

*Half page image nullam nunc eros, vehicula feugiat*