Growing Graceful and Harmonious Trees
Edinah K. Gnang, Isaac Wass

TL;DR
This paper introduces symbolic methods for listing graphs with identical label sequences, confirms a conjecture on graceful labeled trees, and presents a new algorithm for graceful labeling.
Contribution
It provides a constructive approach to enumerate gracefully labeled trees and confirms Whitty's conjecture on determinantal constructions.
Findings
Confirmed Whitty's conjecture on graceful trees
Developed symbolic constructions for graph enumeration
Proposed a new graceful labeling algorithm
Abstract
We describe symbolic constructions for listing and enumerating graphs having the same induced edge label sequence. We settle in the affirmative R. Whitty's [W08] conjectured existence of determinantal constructions for listing and enumerating gracefully labeled trees. We conclude the paper with a description of a new graceful labeling algorithm.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Graph theory and applications · graph theory and CDMA systems
