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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) ]
Keywords: line graph
- MSC 1991:
*05C99 Graph theory
05C75 Structural characterization of types of graphs
Cited in Zbl. reviews...
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Answers 1-1 (of 1)Zentralblatt MATH,
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