2021/08/02 by Maffucci, Riccardo W. · 2 citations
#05C07 #05C10 #05C35 #05C85 #52B05 #52B10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2108.01058
Given vertex valencies admissible for a self-dual polyhedral graph, we describe an algorithm to explicitly construct such a polyhedron. Inputting in the algorithm permutations of the degree sequence can give rise to non-isomorphic graphs. As an application, we find as a function of n≥ 3 the minimal number of vertices for a self-dual polyhedron with at least one vertex of degree i for each 3≤ i≤ n, and construct such polyhedra. Moreover, we find a construction for non-self-dual polyhedral graphs of minimal order with at least one vertex of degree i and at least one i-gonal face for each 3≤ i≤ n.