## On Maximum-Sized Near-Regular and 6Ö{1}-Matroids

- James G. Oxley, Dirk L. Vertigan, Geoff Whittle
- Graphs and Combinatorics
- 1998

1 Excerpt

- Published 1994 in Graphs and Combinatorics

For integers k > 2, the k-line graph Lk(G ) 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. We define iterated k-line graphs by L~(G) := Lk(L~-I(G)), where L~ := G. In this paper the iterated behavior of the k-line graph operator is investigated. It turns out that the behavior is quite different for k = 2 (the well-known line graph case), k = 3, and k > 4.

@article{Le1994IteratedklineG,
title={Iteratedk-line graphs},
author={Van Bang Le and Erich Prisner},
journal={Graphs and Combinatorics},
year={1994},
volume={10},
pages={193-203}
}