7.1 Introduction to Graph Theory
In this first section, 7.1, we'll delve into the basics of Graph Theory, a fascinating branch of mathematics that has been around since the 18th century. Graph Theory is a field of study that focuses on graphs, which are essentially a set of objects (vertices or nodes) that are interconnected by links (edges or arcs). These graphs can be used to model a wide range of real-world systems, including computer networks, social networks, and even biological systems.
When we talk about graphs, we're really referring to two basic components: vertices (or nodes) and edges. Each vertex represents an entity, while each edge represents a relationship or connection between these entities. For example, consider a group of friends. Each friend can be represented as a vertex, and if two friends know each other, we can draw an edge between their corresponding vertices. This same principle can be applied to a multitude of real-world systems, from transportation...