Riccardo W. Maffucci

activity

20162026

most citedNodal intersections for random waves against a segment on the 3-dimensional torus

14 citations · 39 across the 27 of their papers we have counts for

collaborators

31 papers

math.CO2026

A note on generating polyhedra and quadrangulations

Luisa Andreis, Riccardo W. Maffucci, Federico Polito

A polyhedron is a planar, $3$ -connected graph. We iteratively construct all polyhedra (save for pyramids) from a unique starting graph, namely the square pyramid, via two graph tra…

math.CO2026

Automorphism Groups in Extremal Families of Polyhedral Graphs

Riccardo W. Maffucci, Bobby Miraftab

We study automorphism groups in five extremal families of polyhedral graphs. For every $n \geq 14$ , we prove that every minimum-order $3$ -polytopal graph containing a vertex of each d…

math.CO2026

The Facial Common Neighbourhood Graph

Riccardo W. Maffucci

Given a polyhedron (planar, $3$ -connected graph) $G$ , we investigate its common neighbourhood graph con( $G$ ). For cubic ( $3$ -regular) polyhedra, we show that the planarity of con($…

math.CO2025

Common neighbours in planar graphs

Riccardo W. Maffucci

For every positive integer $n$ , we find a complete classification for planar graphs according to the collection of numbers of common neighbours for every $n$ -tuple of distinct vert…

math.CO2025

Classification of polyhedral graphs by numbers of common neighbours

Riccardo W. Maffucci

We propose a classification of polyhedra (planar, $3$ -connected graphs) according to their type i.e., their set of quantities of common neighbours for each pair of distinct vertice…

math.CO2025

Regularity and separation for Sierpiński products of graphs

Riccardo W. Maffucci

The Sierpiński product of graphs generalises the vast and relevant class of Sierpiński-type graphs, and is also related to the classic lexicographic product of graphs. Our first ma…

math.CO2025

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…

math.CO2024

Cancellation and regularity for planar, 3-connected Kronecker products

Ruben De March, Riccardo W. Maffucci

We investigate several properties of Kronecker (direct, tensor) products of graphs that are planar and $3$ -connected (polyhedral, $3$ -polytopal). This class of graphs was recently…

math.CO2024

Generation of $3$ -connected, planar line graphs

Phoebe Hollowbread-Smith, Riccardo W. Maffucci

We classify and construct all line graphs that are $3$ -polytopes (planar and $3$ -connected). Apart from a few special cases, they are all obtained starting from the medial graphs o…

math.CO2024

Classification and Construction of Planar, 3-Connected Kronecker Products

Riccardo W. Maffucci

We give a complete classification of the Kronecker (i.e. direct) product graphs that are planar and $3$ -connected (i.e. $3$ -polytopal). They are all of the form \[H\wedge K_2,\] wh…

math.PR2023

Correlation Structure and Resonant Pairs for Arithmetic Random Waves

Valentina Cammarota, Riccardo-W. Maffucci, Domenico Marinucci +1

The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers [RW08, ORW08]. In this paper we study the corr…

math.CO2023★ 1 cited

On self-duality and unigraphicity for $3$ -polytopes

Riccardo W. Maffucci

Recent literature posed the problem of characterising the graph degree sequences with exactly one $3$ -polytopal (i.e. planar, $3$ -connected) realisation. This seems to be a difficu…

math.CO2023

Rao's Theorem for forcibly planar sequences revisited

Riccardo W. Maffucci

We consider the graph degree sequences such that every realisation is a polyhedron. It turns out that there are exactly eight of them. All of these are unigraphic, in the sense tha…

math.CO2023

On the faces of unigraphic $3$ -polytopes

Riccardo W. Maffucci

A $3$ -polytope is a $3$ -connected, planar graph. It is called unigraphic if it does not share its vertex degree sequence with any other $3$ -polytope, up to graph isomorphism. The c…

math.CO2023

On unigraphic polyhedra with one vertex of degree $p - 2$

Jim Delitroz, Riccardo W. Maffucci

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.…

math.CO2022

Independence numbers of polyhedral graphs

Sébastien Gaspoz, Riccardo W. Maffucci

A polyhedral graph is a $3$ -connected planar graph. We find the least possible order $p (k, a)$ of a polyhedral graph containing a $k$ -independent set of size $a$ for all positive in…

math.CO2022

On smallest $3$ -polytopes of given graph radius

Riccardo W. Maffucci, Niels Willems

The $3$ -polytopes are planar, $3$ -connected graphs. A classical question is, for $r \geq 3$ , is the $2 (r - 1)$ -gonal prism $K_{2} \times C_{2 (r - 1)}$ the unique $3$ -polytope of graph radi…

math.CO2022★ 3 cited

Characterising $3$ -polytopes of radius one with unique realisation

Riccardo W. Maffucci

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\…

math.CO2022

On unigraphic $3$ -polytopes of radius one

Riccardo W. Maffucci

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…

math.PR2021★ 1 cited

Asymptotic distribution of Nodal Intersections for ARW against a Surface

Riccardo W. Maffucci, Maurizia Rossi

We investigate Gaussian Laplacian eigenfunctions (Arithmetic Random Waves) on the three-dimensional standard flat torus, in particular the asymptotic distribution of the nodal inte…

math.CO2021

Self-dual polyhedra of given degree sequence

Riccardo W. Maffucci

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 t…

math.PR2021

On the limiting behaviour of arithmetic toral eigenfunctions

Riccardo W. Maffucci, Alejandro Rivera

We consider a wide class of families $(F_{m})_{m \in N}$ of Gaussian fields on $T^{d} = R^{d} / Z^{d}$ defined by \[F_m:x\mapsto \frac{1}{\sqrt{|Λ_m|}}\sum_{λ…

math.CO2021★ 1 cited

Constructing certain families of $3$ -polytopal graphs

Riccardo W. Maffucci

Let $n \geq 3$ and $r_{n}$ be a $3$ -polytopal graph such that for every $3 \leq i \leq n$ , $r_{n}$ has at least one vertex of degree $i$ . We find the minimal vertex count for $r_{n}$ . We th…

math.CO2021

On polyhedral graphs and their complements

Riccardo Walter Maffucci

We find all polyhedral graphs such that their complements are still polyhedral. These turn out to be all self-complementary.

A note on generating polyhedra and quadrangulations

Automorphism Groups in Extremal Families of Polyhedral Graphs

The Facial Common Neighbourhood Graph

Common neighbours in planar graphs

Classification of polyhedral graphs by numbers of common neighbours

Regularity and separation for Sierpiński products of graphs

Deza graphs and regular polyhedra

Cancellation and regularity for planar, 3-connected Kronecker products

Generation of 3-connected, planar line graphs

Classification and Construction of Planar, 3-Connected Kronecker Products

Correlation Structure and Resonant Pairs for Arithmetic Random Waves

On self-duality and unigraphicity for 3-polytopes

Rao's Theorem for forcibly planar sequences revisited

On the faces of unigraphic 3-polytopes

On unigraphic polyhedra with one vertex of degree p−2

Independence numbers of polyhedral graphs

On smallest 3-polytopes of given graph radius

Characterising 3-polytopes of radius one with unique realisation

On unigraphic 3-polytopes of radius one

Asymptotic distribution of Nodal Intersections for ARW against a Surface

Self-dual polyhedra of given degree sequence

On the limiting behaviour of arithmetic toral eigenfunctions

Constructing certain families of 3-polytopal graphs

On polyhedral graphs and their complements

Generation of $3$ -connected, planar line graphs

On self-duality and unigraphicity for $3$ -polytopes

On the faces of unigraphic $3$ -polytopes

On unigraphic polyhedra with one vertex of degree $p - 2$

On smallest $3$ -polytopes of given graph radius

Characterising $3$ -polytopes of radius one with unique realisation

On unigraphic $3$ -polytopes of radius one

Constructing certain families of $3$ -polytopal graphs