Forbidden subdivision in integral trees
Emanuel Juliano
TL;DR
This paper proves that integral trees, which have all integer eigenvalues, cannot contain a subdivided edge with exactly 7 vertices, revealing a structural restriction related to their spectral properties.
Contribution
It establishes a new spectral restriction on integral trees, specifically ruling out certain subdivided edges with 7 vertices.
Findings
Integral trees cannot contain subdivided edges with 7 vertices.
Spectral properties impose structural limitations on trees.
The result advances understanding of eigenvalue constraints in graph theory.
Abstract
We show that if all the eigenvalues of a tree are integers, then it does not contain a subdivided edge with 7 vertices.
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Taxonomy
TopicsAdvanced Graph Theory Research · Advanced Algebra and Logic