A note on plane trees with decreasing labels
Tsun-Ming Cheung, Luc Devroye, and Marcel K. Goh

TL;DR
This paper investigates the asymptotic bounds for counting labeled plane trees with decreasing labels along root-to-leaf paths and explores an application to eigenvalue calculation of the adjacency matrix.
Contribution
It provides new asymptotic bounds for the number of such labeled trees and demonstrates an application to spectral graph theory.
Findings
Derived asymptotic upper and lower bounds for the count of labeled plane trees
Applied results to compute the largest eigenvalue of a tree's adjacency matrix
Enhanced understanding of label restrictions in combinatorial tree structures
Abstract
This note derives asymptotic upper and lower bounds for the number of planted plane trees on nodes assigned labels from the set with the restriction that on any path from the root to a leaf, the labels must strictly decrease. We illustrate an application to calculating the largest eigenvalue of the adjacency matrix of a tree.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Data Management and Algorithms
