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Graceful labeling for mushroom trees.
- Source :
-
Aequationes Mathematicae . Jun2015, Vol. 89 Issue 3, p719-724. 6p. - Publication Year :
- 2015
-
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]
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 89
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 103002386
- Full Text :
- https://doi.org/10.1007/s00010-014-0259-5