Matching-Type Image-Labelings of Trees

A variety of labelings on trees have emerged in order to attack the Graceful Tree Conjecture, but lack showing the connections between two labelings. In this paper, we propose two new labelings: vertex image-labeling and edge image-labeling, and combine new labelings to form matching-type image-labeling with multiple restrictions. The research starts from the set-ordered graceful labeling of the trees, and we give several generation methods and relationships for well-known labelings and two new labelings on trees.

Automated summary

The study introduces two new labeling methods and combines them to form matching-type image labeling with multiple restrictions. The research starts from set-ordered graceful labeling of trees, providing several generation methods and relationships.