The 3-polytopes are planar, 3-connected graphs. A classical question is, given r≥3, is the 2(r−1)-gonal prism K2×C2(r−1) the unique 3-polytope of graph radius r and smallest size? Under some extra assumptions, we answer this question in the positive.
On smallest 3-polytopes of given graph radius
Maffucci R. W.;
2023-01-01
Abstract
The 3-polytopes are planar, 3-connected graphs. A classical question is, given r≥3, is the 2(r−1)-gonal prism K2×C2(r−1) the unique 3-polytope of graph radius r and smallest size? Under some extra assumptions, we answer this question in the positive.
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