Graceful labeling

In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with some subset of the integers between 0 and m inclusive, such that no two vertices share a label, and 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 Alexander Rosa in a 1967 paper on graph labelings.
A major unproven conjecture in graph theory is the Graceful Tree conjecture or Ringel-Kotzig conjecture, named after Gerhard Ringel and Anton Kotzig, which hypothesizes that all trees are graceful. The Ringel-Kotzig conjecture is also known as the 'graceful labeling conjecture'. Kotzig once called the effort to prove the conjecture a 'disease'.
Video Empire produces videos read aloud. Use the information in this video at your own risk. We cannot always guarantee accuracy.
This video uses material from en.wikipedia.o..., licensed with CC Attribution-ShareAlike 3.0. This video is licensed with CC Attribution-Share-Alike 3.0 creativecommon... In order to adapt this content it is required to comply with the license terms. Image licensing information is available via: en.wikipedia.o...

[@Gabrielisbtwmexican]

what lol?