1. Graceful labeling for mushroom trees.
- Author
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Chan, Tsz, Cheung, Wai, and Ng, Tuen
- Subjects
- *
GRAPH labelings , *GRAPH theory , *INJECTIVE functions , *MATHEMATICS , *CODING theory , *MATHEMATICAL functions - Abstract
One famous open problem in graph theory is the Graceful Tree Conjecture, which states that every finite tree has a graceful labeling. In 1973, Kotzig (Util Math 4:261-290, ) proved that if a leaf of a long enough path is identified with any vertex of an arbitrary tree, the resulting tree is graceful. In this paper, we prove that if the center of a large enough star is identified with any vertex of an arbitrary tree, the resulting tree is graceful, and we also provide an upper bound for the size of the star. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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