- Tytuł:
- Fractional Revival of Threshold Graphs Under Laplacian Dynamics
- Autorzy:
-
Kirkland, Steve
Zhang, Xiaohong - Powiązania:
- https://bibliotekanauki.pl/articles/31552789.pdf
- Data publikacji:
- 2020-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
Laplacian matrix
spectral decomposition
quantum information transfer
fractional revival - Opis:
- We consider Laplacian fractional revival between two vertices of a graph $X$. Assume that it occurs at time \(\tau\) between vertices 1 and 2. We prove that for the spectral decomposition \(L=∑_{r=0}^qθ_rE_r\) of the Laplacian matrix $L$ of $X$, for each $r = 0, 1, . . ., q$, either $E_re_1 = E_re_2$, or $E_re_1 = −E_re_2$, depending on whether \(e^{i\tauθ_r}\) equals to 1 or not. That is to say, vertices 1 and 2 are strongly cospectral with respect to $L$. We give a characterization of the parameters of threshold graphs that allow for Laplacian fractional revival between two vertices; those graphs can be used to generate more graphs with Laplacian fractional revival. We also characterize threshold graphs that admit Laplacian fractional revival within a subset of more than two vertices. Throughout we rely on techniques from spectral graph theory.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 585-600
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł