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graph-theory • Verified reference

Spectral Expansion Routing Lemma

Expander and Ramanujan graph constructions provide sparse graph families with strong connectivity properties useful for robust network topology design.

Assumptions

  • Graph family and regularity are specified.
  • Spectral gap or eigenvalue bound is stated.
  • Routing/security interpretation is separated from pure graph theorem.

Proof Obligations

  • Map pure graph property to DFT routing layer.
  • Define adversarial partition model.
  • Distinguish conductance from cryptographic security.
  • Simulate failure and partition scenarios.

Claim Boundary

Established graph-theoretic references may be cited, but DFT-specific routing/security claims require separate modeling and validation.