Fundamentals of Graph Theory

📋 Course Outline

1. Graph definition and components
2. Graph vocabulary and types
3. Graph properties and characteristics
4. Degree and order of graphs
5. Types of graphs and applications

📖 1. Graph definition and components

🔑 Key Concepts & Definitions

• Graph: An set composed of two parts: a set of points called vertices and a set of segments called edges connecting some pairs of vertices (G = (S, A)).
• Vertices (or nodes): Points in a graph representing entities. They are the fundamental units of the graph.
• Edges (or links): Segments that connect pairs of vertices, representing relationships or connections between entities.

📝 Essential Points

• A graph is characterized by its vertices and edges.
• The set of vertices is often denoted as S = {S1, S2, S3, ..., Sn}.
• The set of edges is often denoted as A = {A1, A2, A3, ..., An}.
• The number of vertices is called the cardinality of S (denoted as s).
• The number of edges is called the cardinality of A (denoted as n).
• A graph can be represented as G = (s, n), where s is the number of vertices and n is the number of edges.

💡 Key Takeaway

A graph is a structure composed of points called vertices and segments called edges that connect some pairs of these vertices, serving as a fundamental model for representing relationships between entities.

📖 2. Graph vocabulary and types

🔑 Key Concepts & Definitions