No perfect state transfer in trees with more than 3 vertices

We prove that the only trees that admit perfect state transfer according to the adjacency matrix model are \(P_2\) and \(P_3\). This answers a question first asked by Godsil in 2012 and proves a conjecture by Coutinho and Liu from 2015.

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Bibliographic Details
Published in:arXiv.org 2023-05
Main Authors: Coutinho, Gabriel, Juliano, Emanuel, Thomás Jung Spier
Format: Article
Language:English
Subjects:
Apexes
Online Access:Get full text
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Summary:We prove that the only trees that admit perfect state transfer according to the adjacency matrix model are \(P_2\) and \(P_3\). This answers a question first asked by Godsil in 2012 and proves a conjecture by Coutinho and Liu from 2015.
ISSN:2331-8422