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 K 2 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.