IB Math AI AHL 3.14 - Graph Theory Notes

IB Maths AI HL 3.14 Notes – Graph Theory

This IB Maths AI HL 3.14 resource introduces the foundations of graph theory and is fully aligned with the IB Applications and Interpretation HL syllabus.

Students learn the structure of graphs and networks, including the meaning of vertices (nodes) and edges and how these represent relationships between objects in a system. The notes explain key vocabulary such as adjacent vertices, adjacent edges, and the degree of a vertex, helping students interpret and analyse graphical network structures.

The resource develops different types of graphs used in mathematical modelling, including simple graphs, complete graphs, weighted graphs, and directed graphs. Students also learn how to identify in-degree and out-degree in directed networks and explore how graphs can represent real-world systems such as transportation networks, computer networks, and social media connections.

Further topics include subgraphs and trees, with clear explanations of how trees are connected graphs with no cycles and exactly one path between any two vertices. These concepts help students understand hierarchical structures and network design.

Structured practice questions guide students through identifying vertices and edges, calculating vertex degree, analysing graph types, and determining properties such as the maximum number of edges in a simple graph.

Ideal for IB Maths AI HL teachers introducing graph theory, network vocabulary, directed graphs, and tree structures within discrete mathematics.