Zobrazeno 1 - 10
of 145
pro vyhledávání: '"Donno, Alfredo"'
We introduce a switching operation, inspired by the Godsil-McKay switching, in order to obtain pairs of $G$-cospectral gain graphs, that are gain graphs cospectral with respect to every representation of the gain group $G$. For instance, for two sign
Externí odkaz:
http://arxiv.org/abs/2207.10986
Publikováno v:
Journal of Algebra 626 (2023), 135-162
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 characterize the associated semigroup, proving that it is isomorphic to the p
Externí odkaz:
http://arxiv.org/abs/2205.09035
Publikováno v:
In Journal of Algebra 1 December 2024 659:148-182
Autor:
Cavaleri, Matteo, Donno, Alfredo
Publikováno v:
Special Matrices, Volume 10 (2022), 343-365
We define $G$-cospectrality of two $G$-gain graphs $(\Gamma,\psi)$ and $(\Gamma',\psi')$, proving that it is a switching isomorphism invariant. When $G$ is a finite group, we prove that $G$-cospectrality is equivalent to cospectrality with respect to
Externí odkaz:
http://arxiv.org/abs/2111.12428
Publikováno v:
European Journal of Combinatorics 102 (2022), 103479
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 and the Beineke's characterization. In particular, we present a list of
Externí odkaz:
http://arxiv.org/abs/2101.09677
For each $p\geq 1$, the star automaton group $\mathcal{G}_{S_p}$ is an automaton group which can be defined starting from a star graph on $p+1$ vertices. We study Schreier graphs associated with the action of the group $\mathcal{G}_{S_p}$ on the regu
Externí odkaz:
http://arxiv.org/abs/2101.07547
Publikováno v:
In Linear Algebra and Its Applications March 2024
Publikováno v:
Linear Algebra and its Applications 613 (2021), 241-270
Let $G$ be an arbitrary group. We define a gain-line graph for a gain graph $(\Gamma,\psi)$ through the choice of an incidence $G$-phase matrix inducing $\psi$. We prove that the switching equivalence class of the gain function on the line graph $L(\
Externí odkaz:
http://arxiv.org/abs/2007.14839
Publikováno v:
Adv. Group Theory Appl. 11 (2021), 75-112
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 its commutator subgroup, contains a free semigroup on two elements and
Externí odkaz:
http://arxiv.org/abs/2007.12871
Publikováno v:
J. Algebr. Comb. 54 (2021), 265-293
We study the balance of $G$-gain graphs, where $G$ is an arbitrary group, by investigating their adjacency matrices and their spectra. As a first step, we characterize switching equivalence and balance of gain graphs in terms of their adjacency matri
Externí odkaz:
http://arxiv.org/abs/2001.08490