Math 2.0

Combinatorics Definition

Edge set

Builds on Graph

Definition

Let GG be a graph with vertex set VV and adjacency relation ∼\sim. The edge set of GG is the set E(G)={{u,v}:u,v∈V, u∼v}E(G) = \{ \{u, v\} : u, v \in V,\ u \sim v \} of unordered pairs of adjacent vertices.

Remarks

Each edge is a 22-element subset of VV, because ∼\sim is irreflexive. The number of edges ∣E(G)∣|E(G)| is the size of GG, and the number of vertices ∣V∣|V| is its order. The handshaking lemma relates ∣E(G)∣|E(G)| to the degrees of the vertices.

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To understand this page from the ground up, read these 2 pages in order. The foundations come first.

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  1. Graph definition
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Where this leads

4 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Glossary_of_graph_theory, E
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