Open AccessSome Results on Generating Graceful Trees
Author(s) -
S. Venkatesh,
K. Balasubramanian
Publication year - 2018
Publication title -
international journal of engineering and technology
Language(s) - English
Resource type - Journals
ISSN - 2227-524X
DOI - 10.14419/ijet.v7i4.10.21283
Subject(s) - vertex (graph theory) , combinatorics , caterpillar , mathematics , graph , tree (set theory) , computer science , discrete mathematics , biology , botany , lepidoptera genitalia
Let and be any two simple graphs. Then is the graph obtained by merging a vertex of each copy of with every attachment vertices of . Let be the one vertex union of copies of the given caterpillar with the common vertex as one of the penultimate vertices. If is any caterpillar, then define . Recursively for , construct ,that is, Here the tree considered for attachment with is a caterpillar, but not necessarily the same among the levels. In this paper we prove that the tree is graceful for