On smallest $3$-polytopes of given graph radius

Riccardo W. Maffucci, Niels Willems

The $3$-polytopes are planar, $3$-connected graphs. A classical question is, for $r\ge 3$, is the $2(r-1)$-gonal prism $K_2\times C_{2(r-1)}$ the unique $3$-polytope of graph radi…