New families of graceful banana trees
type: Item
instance of: scholarly article
title: New families of graceful banana trees
zbMATH Open document ID: 0862.05091
DOI: 10.1007/BF02837173
author: Vasanti N. Bhat-Nayak
author: Ujwala N. Deshmukh
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1996-12-08T00:00:00Z
review text: Let \(G= (V,E)\) be a graph with \(p\) vertices and \(q\) edges. An injective map \(\phi\) from \(V\) into \(\{0,1, \dots, q\}\) is called a graceful labeling of \(G\) if the induced map \(\Phi\) from \(E\) into \(\{1,2, \dots, q\}\), defined by \(\Phi (e) = |\phi (u)- \phi(v) |\) for \(e= uv\), is surjective. If a graceful labeling of a graph \(G\) exists, \(G\) is called a graceful graph. A conjecture due to Ringel and Kotzig is that all trees are graceful. This conjecture is still open. A banana tree is one obtained from a family of stars by joining one end-vertex of each star to a new vertex. In the paper a new family of banana trees is defined and it is shown that the trees in this family are graceful.
Mathematics Subject Classification ID: 05C78
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 955223
zbMATH Keywords: graceful labeling
zbMATH Keywords: graceful graph
zbMATH Keywords: trees
zbMATH Keywords: banana tree
zbMATH Keywords: stars
reviewed by: Dietmar Cieslik
MaRDI profile type: Publication
cites work: Q3347935
description: scientific article; zbMATH DE number 955223