Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.lineGraph

{V : Type u_1} → (G : SimpleGraph V) → SimpleGraph ↑G.edgeSet

The line graph of a simple graph G has its vertex set as the edges of G, and two vertices of the line graph are adjacent if the corresponding edges share a vertex in G.

Defined in
Mathlib.Combinatorics.SimpleGraph.LineGraph
Cited by
7 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SimpleGraph.Copy.toLineGraphEmbedding · cited by 2Copy.toLineGraphEmbeddingSimpleGraph.map_lineGraph_le_of_le · cited by 1SimpleGraph.map_lineGraph…SimpleGraph.Copy.lineGraph · cited by 1Copy.lineGraphSimpleGraph.IsContained.isIndContained_lineGraph · cited by 0IsContained.isIndContaine…SimpleGraph.IsContained.lineGraph · cited by 0IsContained.lineGraphSimpleGraph.lineGraph_adj_iff_exists · cited by 0SimpleGraph.lineGraph_adj…SimpleGraph.lineGraph_bot · cited by 0SimpleGraph.lineGraph_botSimpleGraph.IsIndContained.lineGraph · cited by 0IsIndContained.lineGraphSimpleGraph.Iso.lineGraph · cited by 0Iso.lineGraphSimpleGraph.IsSubgraph.lineGraph · cited by 0IsSubgraph.lineGraphSetLike.coe · cited by 8199SetLike.coeSet.Elem · cited by 7166Set.ElemSimpleGraph · cited by 3072SimpleGraphSet.Nonempty · cited by 2627Set.NonemptySym2 · cited by 737Sym2SimpleGraph.edgeSet · cited by 199SimpleGraph.edgeSetSimpleGraph.lineGraphCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by10

Results whose statement or proof uses this declaration.