Iteratedk-line graphs

Abstract

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.

DOI: 10.1007/BF02986664

4 Figures and Tables

Cite this paper

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