In graph theory, a graceful labeling of a graph with n vertices and e edges is a labeling of its vertices with distinct integers between 0 and e inclusive, such that each edge is uniquely identified by the positive, or absolute difference between its endpoints. A graph which admits a graceful labeling is called a graceful graph. The name "graceful labeling" is due to Solomon W.
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- In graph theory, a graceful labeling of a graph with n vertices and e edges is a labeling of its vertices with distinct integers between 0 and e inclusive, such that each edge is uniquely identified by the positive, or absolute difference between its endpoints. A graph which admits a graceful labeling is called a graceful graph. The name "graceful labeling" is due to Solomon W. Golomb; this class of labelings was originally given the name β-labelings by Alex Rosa in a 1967 paper on graph labelings. A major unproven conjecture in graph theory is the Ringel-Kotzig conjecture, which hypothesizes that all trees are graceful. (The Ringel-Kotzig conjecture is also known as "Von Koch's conjecture" and the "graceful labeling conjecture". ) Kotzig once called the effort to prove the conjecture a "disease".
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- In graph theory, a graceful labeling of a graph with n vertices and e edges is a labeling of its vertices with distinct integers between 0 and e inclusive, such that each edge is uniquely identified by the positive, or absolute difference between its endpoints. A graph which admits a graceful labeling is called a graceful graph. The name "graceful labeling" is due to Solomon W.
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