Strong cospectrality in trees
Gabriel Coutinho, Emanuel Juliano, Thom\'as Jung Spier
TL;DR
This paper proves that in trees, it is impossible to find three vertices that are pairwise strongly cospectral, resolving a question posed by Godsil and Smith in 2017.
Contribution
The paper establishes a new fundamental property of trees regarding strongly cospectral vertices, answering an open question in spectral graph theory.
Findings
No tree contains three pairwise strongly cospectral vertices.
Provides a definitive answer to a 2017 open problem.
Advances understanding of spectral properties in trees.
Abstract
We prove that no tree contains a set of three vertices which are pairwise strongly cospectral. This answers a question raised by Godsil and Smith in 2017.
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Limits and Structures in Graph Theory