DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)audited 2026-08-01

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 spanning-tree number $\tau(G)$

Definition

For a finite graph $G$ , its spanning-tree number is

$\tau(G):=|\{T:T\text{ is a spanning tree of }G\}|.$

This is a natural number because the displayed set is finite (The set of spanning trees of a finite graph is finite, The cardinality $\lvert A\rvert$ of a finite set). In particular, $\tau(G)=0$ exactly when $G$ has no spanning tree.

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 37 results over 15 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

Reinhard Diestel, Graph Theory, Preview Chapter 1 (standard reference, not scraped)
ISI Bangalore discrete mathematics notes, Trees and Cayley’s theorem (standard reference, not scraped)

The spanning-tree number τ(G)\tau(G)τ(G)