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Graph Theory Basics

High School

Definition

A graph is a structure consisting of vertices and edges. It's used to model relationships and networks.

∑_v ∈ V \deg(v) = 2|E|

Handshaking lemma (sum of degrees = 2 × edges)

|V| - |E| + |F| = 2

Euler's formula (planar graphs)

Example 1

How many edges in a complete graph with 5 vertices?

Discovered by: Leonhard Euler (1736)

Euler founded graph theory by solving the Seven Bridges of Königsberg problem.

Friend relationship analysis

Routing algorithms

Shortest path, MST