trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Every vertex an identity Seidel switch

A finite nonempty simple graph has every vertex as an identity Seidel switch if and only if it has one vertex. Edge-count preservation forces regularity, and switching at a vertex changes the degree of each other vertex by one.

Closed Authored exposition
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES0
PROOF DEPTH0
DOCUMENT LINKS0
THEOREM

Exactly the one-vertex graph

RELATIONSHIP ATLAS

Every connection, in context.

Explore in 3D
Direct recorded relationships
Every vertex an identity Seidel switchEvery vertex an identity Seidelswitch
Proof dependencyStructural affinityDocument link

Certified topology / UPSTREAM

Prerequisites

None recorded in this release.

Certified topology / DOWNSTREAM

Consequences

None recorded in this release.

RELATED KNOWLEDGE

Structural connections

None recorded in this release.

Documents & exposition

None recorded in this release.

Other authored & advisory relationships

None recorded in this release.

LIBRARY / RELEASE VERSIONS

Content history

Loading release versions...
Browse the archive

Certified provenance

Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/Graph/SeidelSwitching/VertexIdentitySwitches
Repository path
D5/S3/Combinatorics/Graph/SeidelSwitching/VertexIdentitySwitches.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

Authority boundary

Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.