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

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 k known graceful trees, k≥2 in a specific way. In fact, each member of this new class of trees admits α-labeling, a stronger version of graceful labeling. Consequently, each member of this family of trees decomposes complete graphs and complete bipartite graphs.