Antimagic labeling of new classes of trees

Abstract

An antimagic labeling of a graph G with q edges is an injective mapping such that the induced vertex label for each vertex is different, where the induced vertex label of a vertex u is Here, E(u) is the set of edges incident to the vertex u. In 1990, Hartsfield and Ringel conjectured that all trees except K2 are antimagic. Still this conjecture is open. In this article, we prove that two recursive classes of trees called binomial tree Bk, and Fibonacci tree Fh, are antimagic. This result supports Hartsfield and Ringel conjecture.

Keywords

• graph labeling
• antimagic labeling
• binomial tree
• fibonacci tree
• hartsfield and ringel conjecture