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  "problem_id": "vibemathed:the-delavina-waller-conjecture-on-the-wiener-index",
  "title": "The DeLaViña–Waller conjecture on the Wiener index",
  "canonical_statement": "Every finite simple connected graph $G$ with\n$$\n|V(G)|=2d+1,\\qquad \\operatorname{diam}(G)=d\\ge 3\n$$\nsatisfies\n$$\nW(G)\\le W(C_{2d+1})\n=\\frac{(2d+1)d(d+1)}2.\n$$\nThe 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 $d=4$.",
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      "title": "The DeLaViña–Waller conjecture on the Wiener index",
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