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Graceful Tree Conjecture
In graph theory, a graceful labeling of a Graph (discrete mathematics), graph with edges is a graph labeling, labeling of its Vertex (graph theory), vertices with some subset of the integers from 0 to inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints, such that this magnitude lies between 1 and inclusive.Virginia Vassilevska Williams, Virginia Vassilevska, "Coding and Graceful Labeling of trees." SURF 2001PostScript/ref> A graph which admits a graceful labeling is called a graceful graph. The name "graceful labeling" is due to Solomon W. Golomb; this type of labeling was originally given the name β-labeling by Alexander Rosa in a 1967 paper on graph labelings.. A major conjecture in graph theory is the graceful tree conjecture or Ringel–Kotzig conjecture, named after Gerhard Ringel and Anton Kotzig, and sometimes abbreviated GTC. It hypothesizes that all tree (graph), trees are gracef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graceful Labeling
In graph theory, a graceful labeling of a graph with edges is a labeling of its vertices with some subset of the integers from 0 to inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints, such that this magnitude lies between 1 and inclusive. Virginia Vassilevska, "Coding and Graceful Labeling of trees." SURF 2001PostScript/ref> A graph which admits a graceful labeling is called a graceful graph. The name "graceful labeling" is due to Solomon W. Golomb; this type of labeling was originally given the name β-labeling by Alexander Rosa in a 1967 paper on graph labelings.. A major conjecture in graph theory is the graceful tree conjecture or Ringel–Kotzig conjecture, named after Gerhard Ringel and Anton Kotzig, and sometimes abbreviated GTC. It hypothesizes that all trees are graceful. It is still an open conjecture, although a related but weaker conjecture known as "Ringel's conjecture" was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
