Characterising 3-polytopes of radius one with unique realisation

2022/07/06 by Maffucci, Riccardo W. · 4 citations
#05C07 #05C10 #05C62 #05C75 #52B05 #52B10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2207.02725

Abstract

Let F be a planar, 3-connected graph of radius one on p vertices, with a vertices of degree three. We characterise all unigraphic degree sequences for such graphs, when a≥ 3 and p is large enough with respect to a. This complements the work of \citemafpo4 for a≤ 3.

Cited by

• Common neighbours in planar graphs
• Classification of polyhedral graphs by numbers of common neighbours
• Regularity and separation for Sierpiński products of graphs
• Classification of planar Deza graphs

Related

• On unigraphic 3-polytopes of radius one
• On self-duality and unigraphicity for 3-polytopes
• On smallest 3-polytopes of given graph radius
• On unigraphic polyhedra with one vertex of degree p-2
• Constructing certain families of 3-polytopal graphs