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808.05091
Le Van Bang; Prisner, Erich
Iterated \$k\$-line graphs. (English)
[J] Graphs Comb. 10, No.2, 193-203 (1994). [ISSN 0911-0119]

``For integers \$k \geq 2\$, the \$k\$-line graph 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\$.'' Starting with a graph \$G\$, one can construct the sequence of graphs in which the next term is the \$k\$-line graph of the previous one. These sequences can by divided into the following three types: (i) the graphs in the sequence vanish after finitely many steps; (ii) the graphs do not vanish and no two of them are isomorphic; (iii) the graphs do not vanish and two graphs are isomorphic.\par For any fixed \$k \geq 2\$ and a chosen type, the authors characterize graphs that produce sequences of the prescribed type.
[ L.Soltes (Memphis) ]
MSC 1991:
*05C99 Graph theory
05C75 Structural characterization of types of graphs
Keywords: line graph
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