Abstract
Strong cospectrality is an equivalence relation on the set of vertices of a graph that is of importance in the study of quantum state transfer in graphs. We construct families of abelian Cayley graphs in which the number of mutually strongly cospectral vertices can be arbitrarily large.
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Acknowledgements
This work was partially supported by a grant from the Simons Foundation (#633214 to Peter Sin). I would like to thank Soffia Arnadottir and Chris Godsil for some fruitful discussions. Soffia also helped with some early computer calculations. Thanks also to Ada Chan from whom I first learned of the question on the size of a strong cospectrality class, and to Hermie Monterde for her helpful comments on an earlier version of this paper. Finally, I thank the referees for their thoughtful suggestions to improve the exposition.
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Dedicated to Pham Huu Tiep on the occasion of his 60th birthday.
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Sin, P. Large sets of Strongly Cospectral Vertices in Cayley Graphs. Vietnam J. Math. 52, 411–420 (2024). https://doi.org/10.1007/s10013-023-00625-3
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DOI: https://doi.org/10.1007/s10013-023-00625-3