Structure of Trees with Respect to Nodal Vertex Sets
Asghar Bahmani, Dariush Kiani

TL;DR
This paper investigates the structural properties of trees related to specific adjacency and Laplacian eigenvalues, identifying how eigenvalue multiplicities influence tree structure using $\lambda$-minimal trees.
Contribution
It introduces the concept of $\lambda$-minimal trees to characterize tree structures with given eigenvalue multiplicities and explores their relation to Laplacian eigensystems.
Findings
Characterization of trees with specified adjacency eigenvalue multiplicities
Identification of $\lambda$-minimal trees as structural archetypes
Analysis of the relationship between tree structure and Laplacian eigensystems
Abstract
Let be a tree with a given adjacency eigenvalue . In this paper, by using the -minimal trees, we determine the structure of trees with a given multiplicity of the eigenvalue . Furthermore, we consider the relationship between the structure of trees and the eigensystem of a given Laplacian eigenvalue.
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Taxonomy
TopicsGraph theory and applications · Synthesis and Properties of Aromatic Compounds · Advanced Graph Theory Research
