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Graceful wind
chimes
Jocelyn R. Bell, Lotenna Nwobbi, Connor Parrow, Alexandria Wheeler and Ephrata Zelleke
Vol. 14 (2021), No. 4, 683–696
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Abstract |
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A graceful labeling of a graph with edges is an assignment to each vertex of a unique label between and , inclusive, satisfying the additional requirement that if each edge is labeled by the absolute value of the difference of its incident vertices, then the set of edge labels is exactly . It has been an open question for more than 50 years whether or not every tree has a graceful labeling. In fact, it is unknown whether every tree with maximum degree 3 has a graceful labeling. We introduce a class of trees with maximum degree 3, which we call wind chimes. We prove that all wind chimes satisfying certain criteria have a graceful labeling. |
Keywords
graceful labeling, alpha labeling, graceful tree, wind
chime
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Mathematical Subject Classification
Primary: 05C78
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Milestones
Received: 17 November 2020
Revised: 19 April 2021
Accepted: 19 April 2021
Published: 23 October 2021
Communicated by Joseph Gallian
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Authors |
| Jocelyn R. Bell | |
| Department of Mathematics and
Computer Science Hobart and William Smith Colleges Geneva, NY United States |
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| Lotenna Nwobbi | |
| Department of Mathematics Harvey Mudd College Claremont, CA United States |
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| Connor Parrow | |
| Department of Mathematics and
Computer Science Hobart and William Smith Colleges Geneva, NY United States |
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| Alexandria Wheeler | |
| Department of Mathematics Carthage College Kenosha, WI United States |
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| Ephrata Zelleke | |
| Center for Data, Mathematical &
Computational Sciences Goucher College Baltimore, MD United States |
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