Math 2.0

Combinatorics Definition

Subgraph

Builds on Graph

Definition

Let G=(V,E)G = (V, E) be a graph. A subgraph of GG is a graph H=(V′,E′)H = (V', E') with V′⊆VV' \subseteq V and E′⊆EE' \subseteq E. Each edge of E′E' has both ends in V′V', because HH is a graph.

Remarks

A subgraph is spanning if V′=VV' = V. An induced subgraph keeps all edges of GG between the chosen vertices. In the cycle C4C_4 with vertices 1,2,3,41, 2, 3, 4, the path 1−2−31 - 2 - 3 is a subgraph.

Reading path

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Where this leads

12 pages build on this one.

Further reading

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