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On unigraphic 3-polytopes of radius one

2022/07/05 by Maffucci, Riccardo W.
#05C07 #05C10 #05C30 #05C62 #05C75 #05C85 #52B05 #52B10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2207.02040

Abstract

We ask which degree sequences admit a unique realisation as a 3-polytopal graph (polyhedron) on p vertices. We give an exhaustive list of these sequences for the case where one degree equals p-1 and exactly two or three of them equal 3. We also find all 3-polytopes of radius one with p≤ 17, and those with q≤ 41 edges, by developing a fast algorithm and making use of High Performance Computing.

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