Iterated \(k\)-line graphs
type: Item
instance of: scholarly article
title: Iterated \(k\)-line graphs
zbMATH Open document ID: 0808.05091
DOI: 10.1007/BF02986664
author: Van Bang Le
author: Erich Prisner
published in: Graphs and Combinatorics
publication date: 1994-09-26T00:00:00Z
review text: ``For integers \(k \geq 2\), the \(k\)-line graph of a graph \(G\) is defined as a graph whose vertices correspond to the complete subgraphs on \(k\) vertices in \(G\) with two distinct vertices adjacent if the corresponding complete subgraphs have \(k-1\) common vertices in \(G\).'' Starting with a graph \(G\), one can construct the sequence of graphs in which the next term is the \(k\)-line graph of the previous one. These sequences can by divided into the following three types: (i) the graphs in the sequence vanish after finitely many steps; (ii) the graphs do not vanish and no two of them are isomorphic; (iii) the graphs do not vanish and two graphs are isomorphic. For any fixed \(k \geq 2\) and a chosen type, the authors characterize graphs that produce sequences of the prescribed type.
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 644737
zbMATH Keywords: line graph
reviewed by: Ľubomír Šoltés
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02986664
OpenAlex ID: W2327248052
description: scientific article; zbMATH DE number 644737