Old and new generalizations of line graphs
type: Item
instance of: scholarly article
title: Old and new generalizations of line graphs
zbMATH Open document ID: 1061.05078
DOI: 10.1155/S0161171204310094
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/51250
review text: Summary: Line graphs have been studied for over seventy years. \textit{H. Whitney} [Am. Math. J. 54, 150--168 (1932; Zbl 0003.32804)] showed that for connected graphs, edge-isomorphism implies isomorphism except for \(K_3\) and \(K_{1,3}\). The line graph transformation is one of the most widely studied of all graph transformations. In its long history, the concept has been rediscovered several times, with different names such as derived graph, interchange graph, and edge-to-vertex dual. Line graphs can also be considered as intersection graphs. Several variations and generalizations of line graphs have been proposed and studied. These include the concepts of total graphs, path graphs, and others. In this brief survey we describe these and some more recent generalizations and extensions including super line graphs and triangle graphs.
Mathematics Subject Classification ID: 05C75
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 05C62
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 2168702
author: Jay Bagga
MaRDI profile type: Publication
OpenAlex ID: W1999055138
description: scientific article; zbMATH DE number 2168702