Graph Theory: Fundamentals and Applications
Graph theory is a rich branch of mathematics that studies the properties of graphs—mathematical structures used to model pairwise relations between objects. In this context, a graph is not the familiar coordinate plot, but rather a collection of vertices (or nodes) connected by edges.
Fundamental Concepts
Basic Definitions
- Graph: A graph G = (V, E) consists of a set V of vertices and a set E of edges, where each edge connects a pair of vertices.
- Vertex (Node): A fundamental unit in a graph, often represented as a point or circle.
- Edge: A connection between two vertices, typically drawn as a line.
- Adjacent: Two vertices are adjacent if they are connected by an edge.
- Incident: An edge is incident to a vertex if the vertex is an endpoint of the edge.