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Graph theory basics

Intuition

Understand first, compress later.

Discrete mathematics studies countable structures, combinations, graphs and recursion.

Switch representations

Graph, degrees and the handshake lemma|V| = 5, |E| = 6

vertices (|V| = 5)edges (|E| = 6)degree of the vertex

The degree of a vertex counts the edges meeting it. Adding all degrees counts every edge exactly twice — once at each end. So the sum of the degrees is always twice the number of edges: 12 = 2 · 6. In particular it is always even.

Formal view

You can graph theory basics when you can recognise the underlying objects, select valid rules and check each step for equivalence or logical implication.

Why does it work?

This skill sits on a prerequisite network. If a step is unstable, repair the missing prerequisite instead of merely doing more items of the same type.