Giusy Monzillo

activity

20202026

collaborators

17 papers

math.CO2026

On the combinatorial structure of graphs with a spectral idempotent of small dual diameter

Edwin R. van Dam, Giusy Monzillo, Safet Penjić

Let $Γ$ be a connected regular graph with an eigenvalue $λ$ and corresponding idempotent $E_{λ}$ . Let $E_{λ} = ⟨ J, E_{λ} ⟩^{\circ}$ be the algebra generated by $J$ and $E_λ…

math.CO2025

On the $Q$ -polynomial property of bipartite graphs admitting a uniform structure

Blas Fernández, Roghayeh Maleki, Štefko Miklavič +1

Let $Γ$ denote a finite, connected graph with vertex set $X$ . Fix $x \in X$ and let $ε \geq 3$ denote the eccentricity of $x$ . For mutually distinct scalars $\{θ^*_i\}_{i=…

math.CO2024

The association scheme on the set of flags of a finite generalized quadrangle

Francesco Colangelo, Giusy Monzillo, Alessandro Siciliano

In this paper, the association scheme defined on the flags of a finite generalized quadrangle is considered. All possible fusions of this scheme are listed, and a full description…

math.CO2024

On the $Q$ -polynomial property of the full bipartite graph of a Hamming graph

Blas Fernández, Roghayeh Maleki, Štefko Miklavič +1

The $Q$ -polynomial property is an algebraic property of distance-regular graphs, that was introduced by Delsarte in his study of coding theory. Many distance-regular graphs admit t…

math.CO2024

On combinatorial structure and algebraic characterizations of distance-regular digraphs

Giusy Monzillo, Safet Penić

Let $Γ = Γ (A)$ denote a simple strongly connected digraph with vertex set $X$ , diameter $D$ , and let ${A_{0}, A := A_{1}, A_{2}, \dots, A_{D}}$ denote the set of distance- $i$ matrices of $Γ$ . L…

math.CO2024

On Hoffman polynomials of $λ$ -doubly stochastic irreducible matrices and commutative association schemes

Giusy Monzillo, Safet Penjić

Let $Γ$ denote a finite (strongly) connected regular (di)graph with adjacency matrix $A$ . The {\em Hoffman polynomial} $h (t)$ of $Γ = Γ (A)$ is the unique polynomial of smallest degre…

math.CO2024

Classifying pseudo-ovals, translation generalized quadrangles, and elation Laguerre planes of small order

Giusy Monzillo, Tim Penttila, Alessandro Siciliano

We provide classification results for translation generalized quadrangles of order less or equal to $64$ , and hence, for all incidence geometries related to them. The results consi…

math.CO2023

Distance-regular graphs with classical parameters that support a uniform structure: case $q \geq 2$

Blas Fernández, Roghayeh Maleki, Štefko Miklavič +1

Let $Γ = (X, R)$ denote a finite, simple, connected, and undirected non-bipartite graph with vertex set $X$ and edge set $R$ . Fix a vertex $x \in X$ , and define $\…

math.CO2023

On commutative association schemes and associated (directed) graphs

Giusy Monzillo, Safet Penjić

Let $M$ denote the Bose--Mesner algebra of a commutative $d$ -class association scheme $X$ (not necessarily symmetric), and $Γ$ denote a (strongly) connected (dir…

math.CO2023

Distance-regular graphs with classical parameters that support a uniform structure: case $q \leq 1$

Blas Fernández, Roghayeh Maleki, Štefko Miklavič +1

Let $Γ = (X, R)$ denote a finite, simple, connected, and undirected non-bipartite graph with vertex set $X$ and edge set $R$ . Fix a vertex $x \in X$ , and define $\…

math.CO2023

Classification of spreads of Tits quadrangles of order 64

Giusy Monzillo, Tim Penttila, Alessandro Siciliano

Brown et al. provide a representation of a spread of the Tits quadrangle $T_{2} (O)$ , $O$ an oval of $P G (2, q)$ , $q$ even, in terms of a certain family of $q$ …

math.CO2023

Eggs in finite projective spaces and unitals in translation planes

Giusy Monzillo, Tim Penttila, Alessandro Siciliano

Inspired by the connection between ovoids and unitals arising from the Buekenhout construction in the André/Bruck-Bose representation of translation planes of dimension at most two…

math.CO2022

Reconstructing a generalized quadrangle from the Penttila-Williford $4 -$ class association scheme

Giusy Monzillo, Alessandro Siciliano

Penttila and Williford constructed a $4 -$ class association scheme from a generalized quadrangle with a doubly subtended subquadrangle. We show that an association scheme with appro…

math.CO2022

Reconstructing a generalized quadrangle with a hemisystem from a $4 -$ class association scheme

Giusy Monzillo

In 2013, van Dam, Martin and Muzychuk constructed a cometric $Q -$ antipodal $4 -$ class association scheme from a GQ of order $(t^{2}, t)$ , $t$ odd, which have a hemisystem. In this pap…

math.CO2022

Classification of flocks of the quadratic cone in PG(3,64)

Giusy Monzillo, Tim Penttila, Alessandro Siciliano

Flocks are an important topic in the field of finite geometry, with many relations with other objects of interest. This paper is a contribution to the difficult problem of classify…

math.CO2021

Pseudo-ovals of elliptic quadrics as Delsarte designs of association schemes

John Bamberg, Giusy Monzillo, Alessandro Siciliano

A $p se u d o$ - $o v a l$ of a finite projective space over a finite field of odd order $q$ is a configuration of equidimensional subspaces that is essentially equivalent to a translation…

math.CO2020

On the isomorphism of certain primitive $Q$ -polynomial not $P$ -polynomial association schemes

Giusy Monzillo, Alessandro Siciliano

In 2011, Penttila and Williford constructed an infinite new family of primitive $Q$ -polynomial 3-class association schemes, not arising from distance regular graphs, by exploring t…

On the combinatorial structure of graphs with a spectral idempotent of small dual diameter

On the Q-polynomial property of bipartite graphs admitting a uniform structure

The association scheme on the set of flags of a finite generalized quadrangle

On the Q-polynomial property of the full bipartite graph of a Hamming graph

On combinatorial structure and algebraic characterizations of distance-regular digraphs

On Hoffman polynomials of λ-doubly stochastic irreducible matrices and commutative association schemes

Classifying pseudo-ovals, translation generalized quadrangles, and elation Laguerre planes of small order

Distance-regular graphs with classical parameters that support a uniform structure: case q≥2

On commutative association schemes and associated (directed) graphs

Distance-regular graphs with classical parameters that support a uniform structure: case q≤1

Classification of spreads of Tits quadrangles of order 64

Eggs in finite projective spaces and unitals in translation planes

Reconstructing a generalized quadrangle from the Penttila-Williford 4−class association scheme

Reconstructing a generalized quadrangle with a hemisystem from a 4−class association scheme

Classification of flocks of the quadratic cone in PG(3,64)

Pseudo-ovals of elliptic quadrics as Delsarte designs of association schemes

On the isomorphism of certain primitive Q-polynomial not P-polynomial association schemes

On the $Q$ -polynomial property of bipartite graphs admitting a uniform structure

On the $Q$ -polynomial property of the full bipartite graph of a Hamming graph

On Hoffman polynomials of $λ$ -doubly stochastic irreducible matrices and commutative association schemes

Distance-regular graphs with classical parameters that support a uniform structure: case $q \geq 2$

Distance-regular graphs with classical parameters that support a uniform structure: case $q \leq 1$

Reconstructing a generalized quadrangle from the Penttila-Williford $4 -$ class association scheme

Reconstructing a generalized quadrangle with a hemisystem from a $4 -$ class association scheme

On the isomorphism of certain primitive $Q$ -polynomial not $P$ -polynomial association schemes