Antimagic labeling of new classes of trees. Issue 2 (4th May 2021)

• Record Type: Journal Article
• Authors: Sethuraman, G.; Shermily, K. M.
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 18:Issue 2(2021)
• Page Start: 110
• Page End: 116
• Publication Date: 2021-05-04
• Subjects: Graph labeling -- antimagic labeling -- binomial tree -- Fibonacci tree -- Hartsfield and Ringel conjecture; 05C78
• DOI: 10.1080/09728600.2021.1964334
• Languages: English
• ISSNs: 0972-8600

Abstract

Abstract: An antimagic labeling of a graph G with q edges is an injective mapping f : E ( G ) → { 1, 2, …, q } such that the induced vertex label for each vertex is different, where the induced vertex label of a vertex u is ϕ f ( u ) = ∑ e ∈ E ( u ) f ( e ) . 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, k ≥ 2 and Fibonacci tree Fh, h ≥ 2 are antimagic. This result supports Hartsfield and Ringel conjecture.