Geodesic
CENTERS IN ITERATED LINE GRAPHS
Acta mathematica Universitatis Comenianae, Tome 61 (1992) no. 2 
M. Knor; L. Niepel; L. Soltes. CENTERS IN ITERATED LINE GRAPHS. Acta mathematica Universitatis Comenianae, Tome 61 (1992) no. 2. http://geodesic.mathdoc.fr/item/AMUC_1992_61_2_a9/
@article{AMUC_1992_61_2_a9,
     author = {M. Knor and L. Niepel and L. Soltes},
     title = {CENTERS {IN} {ITERATED} {LINE} {GRAPHS}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1992},
     volume = {61},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1992_61_2_a9/}
}
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AU  - L. Soltes
TI  - CENTERS IN ITERATED LINE GRAPHS
JO  - Acta mathematica Universitatis Comenianae
PY  - 1992
VL  - 61
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AMUC_1992_61_2_a9/
ID  - AMUC_1992_61_2_a9
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%A L. Niepel
%A L. Soltes
%T CENTERS IN ITERATED LINE GRAPHS
%J Acta mathematica Universitatis Comenianae
%D 1992
%V 61
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_1992_61_2_a9/
%F AMUC_1992_61_2_a9

Voir la notice de l'article provenant de la source Comenius University

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 $i\ge 3$.