2023/01/19 by Jim Delitroz, Delitroz, Jim, Riccardo W. Maffucci +1 · 1 citation
Computer Science · Engineering · #05C07 #05C10 #05C30 #05C62 #05C75 #52B05 #52B10 #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2301.08021
openalex publication_date 2023/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A sequence σ of p non-negative integers is unigraphic if it is the degree sequence of exactly one graph, up to isomorphism. A polyhedral graph is a 3-connected, planar graph. We investigate which sequences are unigraphic with respect to the class of polyhedral graphs, meaning that they admit exactly one realisation as a polyhedron. We focus on the case of sequences with largest entry p-2. We give a classification of polyhedral unigraphic sequences starting with p-2,p-2, as well as those starting with p-2 and containing exactly one 3. Moreover, we characterise the unigraphic sequences where a few vertices are of high degree. We conclude with a few other examples of families of unigraphic polyhedra.