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Connectivity of path graphs

Martin Knor;  L'udovít Niepel — 2000

Discussiones Mathematicae Graph Theory

We prove a necessary and sufficient condition under which a connected graph has a connected P₃-path graph. Moreover, an analogous condition for connectivity of the Pₖ-path graph of a connected graph which does not contain a cycle of length smaller than k+1 is derived.

Radii and centers in iterated line digraphs

Martin Knor;  L'udovít Niepel — 1996

Discussiones Mathematicae Graph Theory

We show that the out-radius and the radius grow linearly, or "almost" linearly, in iterated line digraphs. Further, iterated line digraphs with a prescribed out-center, or a center, are constructed. It is shown that not every line digraph is admissible as an out-center of line digraph.

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