feat(Archive): voltage graphs on K₂, Heawood and Möbius-Kantor graphs

[RaggedR]

This defines voltageGraphK2, a cubic covering construction on K₂ with cyclic voltage group ZMod m. Vertices are Fin 2 × ZMod m, with edges (0, g) ~ (1, g + vⱼ) for three voltages.

Two instances are provided. The Heawood graph (F014A) is voltageGraphK2 7 0 4 6, the Levi graph of the Fano plane PG(2,2): 14 vertices, cubic, girth 6, equal to Sab(G₄₂, C₃) where G₄₂ = Z₇ ⋊ Z₆. The Möbius-Kantor graph (F016A) is voltageGraphK2 8 0 1 3, the generalised Petersen graph GP(8,3): 16 vertices, cubic, girth 6, equal to Sab(GL(2,3), C₃).

Both quotient to K₂ under the fibre projection Prod.fst, recovering the base graph.

The voltage graph construction and named graph instances follow Langer, arXiv:1306.4798, and Gross & Tucker, Topological Graph Theory.

Depends on #39551 (quotient graphs and Lorimer's theorem).

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LLM tools were used to assist with Lean formalization. The mathematical content is the author's own work.

[RaggedR]

Could a maintainer please add the LLM-generated and t-combinatorics labels? Thank you.

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PR summary 7c657ef3ec

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Combinatorics.SimpleGraph.Action (new file)	644
Mathlib.Combinatorics.SimpleGraph.CosetGraph (new file)	837
Mathlib.Combinatorics.SimpleGraph.Representation (new file)	838
Mathlib.Combinatorics.SimpleGraph.Symmetric (new file)	839
Mathlib.Combinatorics.SimpleGraph.QuotientGraph (new file)	962

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Declarations diff (regex)

+ GraphAction
+ IsArcTransitive
+ IsConnectionSet
+ IsLocallyTransitive
+ IsVertexTransitive
+ SimpleGraph.cosetGraph
+ SimpleGraph.quotientGraph
+ adj_mk
+ adj_smul_iff
+ connectionSet
+ connectionSet_eq_doubleCoset
+ cosetQuotientMap
+ cosetQuotientMap_mk
+ disjoint_stabilizer
+ doubleCoset_isConnectionSet
+ double_coset_stable
+ expandConnectionSet
+ expandConnectionSet_isConnectionSet
+ graphAction
+ heawoodG
+ heawoodS_mem
+ heawoodSabidussiIso
+ heawoodSwap
+ heawoodSwap_adj
+ heawoodT_mem
+ heawoodTranslation
+ heawoodTranslation_adj
+ heawoodVoltage
+ heawoodVoltage_directedEdges
+ heawoodVoltage_quotient_complete
+ heawoodVoltage_regular
+ heawoodWitElem
+ heawoodWitElem_correct
+ heawoodWitElem_mem
+ instance : DecidableRel (heawoodVoltage.quotientGraph
+ instance : DecidableRel (mobiusKantorVoltage.quotientGraph
+ instance : DecidableRel heawoodVoltage.Adj := by
+ instance : DecidableRel mobiusKantorVoltage.Adj := by
+ instance : GraphAction heawoodG (Fin 2 × ZMod 7) heawoodVoltage
+ instance : GraphAction mkG (Fin 2 × ZMod 8) mobiusKantorVoltage
+ instance : MulAction heawoodG (Fin 2 × ZMod 7)
+ instance : MulAction mkG (Fin 2 × ZMod 8)
+ instance : MulAction.IsPretransitive heawoodG (Fin 2 × ZMod 7)
+ instance : MulAction.IsPretransitive mkG (Fin 2 × ZMod 8)
+ inv_eq_self_of_sq_eq_one
+ inv_mem
+ isArcTransitive_of_vertexTransitive_locallyTransitive
+ isConnectionSet
+ locallyTransitive_at_one
+ locallyTransitive_everywhere
+ lorimer_forward
+ lorimer_reverse
+ mkG
+ mkS_mem
+ mkSabidussiIso
+ mkSwap
+ mkSwap_adj
+ mkT_mem
+ mkTranslation
+ mkTranslation_adj
+ mkWitElem
+ mkWitElem_correct
+ mkWitElem_mem
+ mobiusKantorVoltage
+ mobiusKantorVoltage_directedEdges
+ mobiusKantorVoltage_quotient_complete
+ mobiusKantorVoltage_regular
+ quotient_cosetGraph_iso
+ sabidussiEquiv
+ sabidussiEquiv_smul
+ sabidussiEquiv_symm_mk
+ sabidussiIso
+ sabidussiSymmetricGraph
+ stabilizer_transitive_on_neighbors
+ toIso
+ toIso_apply
+ toIso_mul
+ toIso_symm
+ voltageGraphK2
++ isVertexTransitive
++ one_not_mem

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean -- pending)

Computed after the build finishes.

---

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (5.00, 0.00)

Current number	Change	Type (weak)
4995	5	exposed public sections

Current commit 7c657ef3ec
Reference commit 88d006abbc

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[RaggedR]

LLM-generated

[RaggedR]

Please add the LLM-generated label to this PR.

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