MCA 520: Graph Theory Instructor Neelima Gupta

Table of Contents Introduction

Origin of Graph Theory Konigsberg Bridge Problem: City of Konigsberg was located on the Pregel river in Prussia. The city occupied the islands of Kneiphopf and the areas of both the banks of the river. Regions linked by 7 bridges. Citizens want to start from home and come back traversing each bridge exactly once.

Models Acquaintance Relations: Invite for a dinner so that everybody knows everybody else Clique Conflict Relations: Invite for a dinner so that there is no conflict amongst the people. Independent Set Job Assignments Bipartite Matching Scheduling Committees in rooms Graph Coloring

Models Contd… Maps Coloring Coloring Road Networks/ Communication Networks MST and TSP

Matrices: Graph Representation Adjacency Matrices Incidence Matrices