Integral trees with given nullity
E. Ghorbani, A. Mohammadian, B. Tayfeh-Rezaie
TL;DR
This paper proves that for any nullity greater than 1, only finitely many integral trees exist, and it establishes the uniqueness of integral trees with nullity 2 and 3.
Contribution
It demonstrates finiteness of integral trees for nullity > 1 and proves the uniqueness of integral trees with nullity 2 and 3.
Findings
Finiteness of integral trees for nullity > 1.
Uniqueness of integral trees with nullity 2.
Uniqueness of integral trees with nullity 3.
Abstract
A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. We prove that for a given nullity more than 1, there are only finitely many integral trees. It is also shown that integral trees with nullity 2 and 3 are unique.
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Taxonomy
TopicsGraph theory and applications · Finite Group Theory Research · Matrix Theory and Algorithms