ITERATED K-LINE GRAPHS

For integers k greater-than-or-equal-to 2, the k-line graph L(k)(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(k)n(G):= L(k)(L(k)n-1(G)), where L(k)0(G):= 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 greater-than-or-equal-to 4.