5 papers
State Transfer and Readout Times for Trees of Diameter 4
Stephen Kirkland, Christopher M. van Bommel
We consider the state transfer properties of continuous time quantum walks on trees of diameter 4. We characterize all pairs of strongly cospectral vertices in trees of diameter 4,…
Eternal Distance-2 Domination in Trees
Alexander Clow, Christopher M van Bommel
We consider the eternal distance-2 domination problem, recently proposed by Cox, Meger, and Messinger, on trees. We show that finding a minimum eternal distance-2 dominating set of…
Quantum walks do not like bridges
Gabriel Coutinho, Chris Godsil, Emanuel Juliano +1
We consider graphs with two cut vertices joined by a path with one or two edges, and prove that there can be no quantum perfect state transfer between these vertices, unless the gr…
State Transfer on Paths with Weighted Loops
Stephen Kirkland, Christopher M. van Bommel
We consider the fidelity of state transfer on an unweighted path on vertices, where a loop of weight has been appended at each of the end vertices. It is known that if …
Pretty good state transfer between internal nodes of paths
Gabriel Coutinho, Krystal Guo, Christopher M. van Bommel
We study a continous-time quantum walk on a path graph. In this paper, we show that, for any odd prime and positive integer , the path on vertices admits pretty…