Theorems · Inductive type · combinatorics
SimpleGraph
Type u → Type u
A simple graph is an irreflexive symmetric relation Adj on a vertex type V.
The relation describes which pairs of vertices are adjacent.
There is exactly one edge for every pair of adjacent vertices;
see SimpleGraph.edgeSet for the corresponding edge set.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Basic
- Cited by
- 3,072 results in Mathlib
- Foundations
- Depth 0 from the axioms, rests on 1 definitions · uses no axioms
Around this declaration
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by3,601
Results whose statement or proof uses this declaration.
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.Walkstatement · cited by 915
- SimpleGraph.Subgraphstatement · cited by 326
- SimpleGraph.Walk.supportstatement and proof · cited by 307
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.Walk.lengthstatement and proof · cited by 212
- SimpleGraph.Subgraph.vertsstatement and proof · cited by 210
- SimpleGraph.edgeSetstatement and proof · cited by 199
- SimpleGraph.Subgraph.Adjstatement and proof · cited by 147
- SimpleGraph.Walk.edgesstatement and proof · cited by 145
- SimpleGraph.Reachablestatement and proof · cited by 141
- SimpleGraph.Walk.IsPathstatement · cited by 140
Showing the 200 most cited of 3,601.