Alphabeta Math
DefinitionDefinition: AI-adaptedProof: Not applicableaudited 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), its line graph L(G) has vertex set E. Distinct vertices e,f∈E are adjacent in L(G) exactly when the edges e and f of G share an endpoint, that is, when e∩f≠∅.

Because E is finite and adjacency is recorded as a set of two-element subsets of E, 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 G has become adjacency in L(G).

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources