The joint sum of graceful trees
type: Item
instance of: scholarly article
title: The joint sum of graceful trees
zbMATH Open document ID: 0795.05044
DOI: 10.1016/0898-1221(93)90027-S
author: Dejun Jin
author: Sizhang Liu
author: Hailou Liu
author: Xiguan Lu
author: Dazhi Zhang
author: Sang-Ho Lee
publication date: 1994-09-11T00:00:00Z
review text: A graph is called graceful, if there is a labeling \(f\) of its vertices with distinct integers so that the induced edge labeling \(f'\) defined by \(f'(u,v) = | f(u) - f(v) |\) assigns each edge a different label. In 1966 A. Rosa conjectured that any tree is graceful. The present paper defines the concept of joint sum of graceful trees: Two trees \(T\) and \(T'\) define the joint sum of \(T\) and \(T'\) as a new tree by connecting a vertex of \(T\) with a vertex of \(T'\). The paper studies the gracefulness of the joint sum of graceful trees and gives necessary and sufficient conditions for a certain family of trees.
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C78
zbMATH DE Number: 571470
zbMATH Keywords: labeling
zbMATH Keywords: graceful trees
zbMATH Keywords: joint sum
reviewed by: Dietmar Cieslik
MaRDI profile type: Publication
cites work: Q5589124
cites work: Q4044627
cites work: Q5422499
Wikidata QID: Q126667898
full work available at URL: 0898-1221(93)90027-s
OpenAlex ID: W1983333112
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 571470