CENTERS IN ITERATED LINE GRAPHS
M. KNOR, L. NIEPEL and L. SOLTES
Abstract.
For a graph $G$ such that $L^2(G)$ is not empty, we construct a supergraph $H$ such that $C(L^i(H))=L^i(G)$ for all $i$, $0\le i\le 2$. Here $L^i(G)$ denotes the $i$-iterated line graph of $G$ and $C(G)$ denotes the subgraph of $G$ induced by central nodes. This result is, in a sense, best possible since we provide an infinite class of graphs $G$ such that $L^i(G)\ne C(L^i(H))$ for any graph $H\supseteq G$ and all $i\ge 3$.
Compressed Postscript 
