Some Results on Generating Graceful Trees - Venkatesh, S.; Balasubramanian, K. (International Journal of Engineering and Technology, 2018)
Let Â and Â be any two simple graphs. Then Â is the graph obtained by merging a vertex of each copy of Â with every attachment vertices of . Let Â be the one vertex union of copies of the given caterpillar Â with the common vertex as one of the penultimate vertices. If Â is any caterpillar, then define . Recursively for , construct ,that is, Â Â Here the tree Â considered for attachment with Â is a caterpillar, but not necessarily the same among the levels. In this paper we prove that the tree Â is graceful forÂ