All lobsters with perfect matchings are graceful

• Author(s) / Creator(s)

  • Morgan, David

• Technical report TR05-01. Given a tree T consider one of its longest paths PT. We define T to be m-distant if all of its vertices are a distance at most m from PT. We will show that any 3-distant tree satisfying both of the following properties is graceful. The tree has a perfect matching. The tree can be constructed by attaching paths of length two to the vertices of a 1-distant tree (caterpillar); these attachments are made by identifying an end vertex of each path of length two with a vertex of the 1-distant tree. | TRID-ID TR05-01

• Date created

  2005

• Subjects / Keywords

  • Lobster
  • Graceful labelling
  • Perfect matching

• Type of Item

  Report

• DOI

  https://doi.org/10.7939/R38P5VB4W

• License

  Attribution 3.0 International