Fractional revival of threshold graphs under Laplacian dynamics
| dc.contributor.author | Kirkland, S. | |
| dc.contributor.author | Zhang, X. | |
| dc.date.accessioned | 2020-02-10T17:16:30Z | |
| dc.date.available | 2020-02-10T17:16:30Z | |
| dc.date.issued | 2020 | |
| dc.date.submitted | 2020-01-23T18:50:09Z | en_US |
| dc.description.abstract | 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 $L = \sum_{r=0}^q \theta_rE_r$ of the Laplacian matrix $L$ of $X$, for each $r = 0, 1, \ldots , q$, either $E_re_1 = E_re_2$, or $E_re_1 = −E_re_2$, depending on whether $e^{i \tau \theta_r}$ 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. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/34539 | |
| dc.publisher | Discussiones Mathematicae Graph Theory | en_US |
| dc.rights | open access | en_US |
| dc.status | yes | |
| dc.subject | Laplacian matrix | en_US |
| dc.subject | Spectral decomposition | en_US |
| dc.subject | Quantum information transfer | en_US |
| dc.subject | Fractional revival | en_US |
| dc.title | Fractional revival of threshold graphs under Laplacian dynamics | en_US |
| dc.type | Article | en_US |