14 citations · 89 across the 13 of their papers we have counts for
16 papers
Godsil-McKay switchings for gain graphs
Matteo Cavaleri, Alfredo Donno, Stefano Spessato
We introduce a switching operation, inspired by the Godsil-McKay switching, in order to obtain pairs of -cospectral gain graphs, that are gain graphs cospectral with respect to…
On a class of poly-context-free groups generated by automata
Matteo Cavaleri, Daniele D'Angeli, Alfredo Donno +1
This paper deals with graph automaton groups associated with trees and some generalizations. We start by showing some algebraic properties of tree automaton groups. Then we charact…
On cospectrality of gain graphs
Matteo Cavaleri, Alfredo Donno
We define -cospectrality of two -gain graphs and , proving that it is a switching isomorphism invariant. When is a finite group, we prove that -cospec…
On an uncountable family of graphs whose spectrum is a Cantor set
Matteo Cavaleri, Daniele D'Angeli, Alfredo Donno +1
For each , the star automaton group is an automaton group which can be defined starting from a star graph on vertices. We study Schreier graphs a…
Characterizations of line graphs in signed and gain graphs
Matteo Cavaleri, Daniele D'Angeli, Alfredo Donno
We generalize three classical characterizations of line graphs to line graphs of signed and gain graphs: the Krausz's characterization, the van Rooij and Wilf's characterization an…
Gain-line graphs via -phases and group representations
Matteo Cavaleri, Daniele D'Angeli, Alfredo Donno
Let be an arbitrary group. We define a gain-line graph for a gain graph through the choice of an incidence -phase matrix inducing . We prove that the switching eq…
Graph automaton groups
Matteo Cavaleri, Daniele D'Angeli, Alfredo Donno +1
In this paper we define a way to get a bounded invertible automaton starting from a finite graph. It turns out that the corresponding automaton group is regular weakly branch over…
A group representation approach to balance of gain graphs
Matteo Cavaleri, Daniele D'Angeli, Alfredo Donno
We study the balance of -gain graphs, where is an arbitrary group, by investigating their adjacency matrices and their spectra. As a first step, we characterize switching eq…
Constructing cospectral signed graphs
Francesco Belardo, Maurizio Brunetti, Matteo Cavaleri +1
A well--known fact in Spectral Graph Theory is the existence of pairs of isospectral nonisomorphic graphs (known as PINGS). The work of A.J. Schwenk (in 1973) and of C. Godsil and…
Distance-balanced graphs and Travelling Salesman Problems
Matteo Cavaleri, Alfredo Donno
For every probability we define a distance-based graph property, the TS-distance-balancedness, that in the case coincides with the standard distance-balancedne…
Permutational powers of a graph
Matteo Cavaleri, Daniele D'Angeli, Alfredo Donno
This paper introduces a new graph construction, the permutational power of a graph, whose adjacency matrix is obtained by the composition of a permutation matrix with the adjacency…
Partial Word and Equality problems and Banach densities
Angela Carnevale, Matteo Cavaleri
We investigate partial Equality and Word Problems for finitely generated groups. After introducing Upper Banach (UB) density on free groups, we prove that solvability of the Equali…
Some degree and distance-based invariants of wreath products of graphs
Matteo Cavaleri, Alfredo Donno
The wreath product of graphs is a graph composition inspired by the notion of wreath product of groups, with interesting connections with Geometric Group Theory and Probability. Th…
Two special subgroups of the universal sofic group
Matteo Cavaleri, Radu B. Munteanu, Liviu Paunescu
We define a subgroup of the universal sofic group, obtained as the normaliser of a separable abelian subalgebra. This subgroup can be obtained as an extension by the group of autom…
Følner functions and the generic Word Problem for finitely generated amenable groups
Matteo Cavaleri
We introduce and investigate different definitions of effective amenability, in terms of computability of Følner sets, Reiter functions, and Følner functions. As a consequence, we…
Computability of Følner sets
Matteo Cavaleri
We define the notion of computability of Følner sets for finitely generated amenable groups. We prove, by an explicit description, that the Kharlampovich group, a finitely presente…