Alphabeta Math
DefinitionDefinition: AI-adaptedProof: Not applicableSession-authored (Fable 5 assisted)audited 2026-07-31
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The line graph whose vertices are the edges of the original graph and whose adjacency records a shared endpoint

Definition

For a graph G=(V,E)G=(V,E), its line graph L(G)L(G) has vertex set EE. Distinct vertices e,f∈Ee,f\in E are adjacent in L(G)L(G) exactly when the edges ee and ff of GG share an endpoint, that is, when e∩f≠∅e\cap f\ne\varnothing.

Because EE is finite and adjacency is recorded as a set of two-element subsets of EE, the line graph is again a finite simple graph (A finite simple graph is a finite vertex set together with a set of two-element vertex subsets). Incidence in GG has become adjacency in L(G)L(G).

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 10 results over 8 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources