MathDBThe odd-graceful tree conjecture
The odd-graceful tree conjecture
An odd-graceful labeling is the tree-labeling notion in which the edge labels are the required distinct odd values. Odd-graceful tree conjecture. Every tree admits an odd-graceful labeling; in the source's notation, . The source attributes this conjecture to Gnanajothi and gives no resolution, so it remains open.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Sources & referencesView supporting material
Primary source
Bing Yao, Chao Yang, Xia Liu, Fei Ma, Jing Su, Hui Sun, Xiaohui Zhang and Yarong Mu, “Strings And Colorings Of Topological Coding Towards Asymmetric Topology Cryptography”, arXiv:2209.15312 (2022).
Additional references
3 papers in this index state this conjecture (2018–2022). The statement above is taken from the most recent of them; the others are arXiv:1807.01188, arXiv:1807.01203.
Source: https://arxiv.org/abs/2209.15312
Gnanajothi (1991), cited in the source as R-B-Gnanajothi-1991
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