Geodesic
Laplacian fractional revival on graphs
The electronic journal of combinatorics, Tome 28 (2021) no. 3
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We develop the theory of fractional revival in the quantum walk on a graph using its Laplacian matrix as the Hamiltonian. We first give a spectral characterization of Laplacian fractional revival, which leads to a polynomial time algorithm to check this phenomenon and find the earliest time when it occurs. We then apply the characterization theorem to special families of graphs. In particular, we show that no tree admits Laplacian fractional revival except for the paths on two and three vertices, and the only graphs on a prime number of vertices that admit Laplacian fractional revival are double cones. Finally, we construct, through Cartesian products and joins, several infinite families of graphs that admit Laplacian fractional revival; some of these graphs exhibit polygamous fractional revival.
DOI : 10.37236/10146
Classification : 05C50, 05C81, 81P68, 05C75, 05C76
Mots-clés : Laplacian matrix, Laplacian fractional revival 
@article{10_37236_10146,
     author = {Ada  Chan and Bobae Johnson and Mengzhen Liu and Malena Schmidt and Zhanghan Yin and Hanmeng Zhan},
     title = {Laplacian fractional revival on graphs},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {3},
     doi = {10.37236/10146},
     zbl = {1470.05100},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10146/}
}
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Ada  Chan; Bobae Johnson; Mengzhen Liu; Malena Schmidt; Zhanghan Yin; Hanmeng Zhan. Laplacian fractional revival on graphs. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/10146

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