Construction of an -labeled tree from a given set of -labeled trees

Abstract

Inspired by the method of Koh et al. (1979) of combining known graceful trees to construct bigger graceful trees, a new class of graceful trees is constructed from a set of known graceful trees, in a specific way. In fact, each member of this new class of trees admits -labeling, a stronger version of graceful labeling. Consequently, each member of this family of trees decomposes complete graphs and complete bipartite graphs.

Keywords

• graceful tree
• graceful tree conjecture
• graceful labeling