The DeLaViña–Waller conjecture on the Wiener index

Precise statement

Every finite simple connected graph $G$ with $$ |V(G)|=2d+1,\qquad \operatorname{diam}(G)=d\ge 3 $$ satisfies $$ W(G)\le W(C_{2d+1}) =\frac{(2d+1)d(d+1)}2. $$ The claimed equality cases are exactly $C_{2d+1}$ for every $d\ge3$, the double star $D_{2,3}$ when $d=3$, and the nine-vertex tree $T_{1,2,2}=S(2,3,3)$ when $d=4$.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.6 Sol; Claude Fable 5

The models assisted in developing proof strategies and checking computations.

Provider: OpenAI, Anthropic · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

No verification note supplied.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-08-19

   The DeLaViña–Waller conjecture on the Wiener index

   VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• The source status is candidate and must not be represented as solved.
• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.