From the 1 of 10 linked papers with an AI index.
10 papers
Automorphism Groups in Extremal Families of Polyhedral Graphs
Riccardo W. Maffucci, Bobby Miraftab
The paper investigates automorphism groups of several extremal families of polyhedral (planar 3‑polytopal) graphs, proving asymmetry for minimal graphs with a full range of vertex…
The Facial Common Neighbourhood Graph
Riccardo W. Maffucci
Given a polyhedron (planar, -connected graph) , we investigate its common neighbourhood graph con(). For cubic (-regular) polyhedra, we show that the planarity of con($…
Deza graphs and regular polyhedra
Riccardo W. Maffucci
We classify all regular polyhedra according to their type i.e., the collection of numbers of common neighbours that any pair of distinct vertices may have (polyhedra are planar, $3…
Common neighbours in planar graphs
Riccardo W. Maffucci
For every positive integer , we find a complete classification for planar graphs according to the collection of numbers of common neighbours for every -tuple of distinct vert…
Classification of polyhedral graphs by numbers of common neighbours
Riccardo W. Maffucci
We propose a classification of polyhedra (planar, -connected graphs) according to their type i.e., their set of quantities of common neighbours for each pair of distinct vertice…
On self-duality and unigraphicity for -polytopes
Riccardo W. Maffucci
Recent literature posed the problem of characterising the graph degree sequences with exactly one -polytopal (i.e. planar, -connected) realisation. This seems to be a difficu…