A dynamic survey of graph labeling
type: Item
instance of: scholarly article
title: A dynamic survey of graph labeling
zbMATH Open document ID: 0953.05067
author: Joseph A. Gallian
published in: The Electronic Journal of Combinatorics
publication date: 1998-04-02T00:00:00Z
full work available at URL: Surveys
review text: Summary: A vertex labeling of a graph \(G\) is an assignment \(f\) of labels to the vertices of \(G\) that induces for each edge \(xy\) a label depending on the vertex labels \(f(x)\) and \(f(y)\). The two best known labeling methods are called graceful and harmonious labelings. A function \(f\) is called a graceful labeling of a graph \(G\) with \(q\) edges if \(f\) is an injection from the vertices of \(G\) to the set \(\{0,1,\ldots,q\}\) such that, when each edge \(xy\) is assigned the label \({\mid}{f(x) - f(y)}{\mid}\), the resulting edge labels are distinct. A function \(f\) is called harmonious if it is an injection from the vertices of \(G\) to the group of integers modulo \(q\) such that when each edge \(xy\) is assigned the label \(f(x) + f(y)\) (mod \(q\)), the resulting edge labels are distinct. When \(G\) is a tree, exactly one label may be used on two vertices. Over the past three decades many variations of graceful and harmonious labelings have evolved and about 200 papers have been on the subject of graph labeling. In this article we survey what known about the various methods.
Mathematics Subject Classification ID: 05C78
Mathematics Subject Classification ID: 05-02
zbMATH DE Number: 1136799
zbMATH Keywords: graceful labeling
zbMATH Keywords: harmonious labelings
zbMATH Keywords: graph labeling
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1136799