Wyniki wyszukiwania

1

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Histories in path graphs

100%

Niepel L.

Discussiones Mathematicae Graph Theory

|

2007

|

tom 27

|

nr 2

345-357

EN

For a given graph G and a positive integer r the r-path graph, $P_r(G)$, has for vertices the set of all paths of length r in G. Two vertices are adjacent when the intersection of the corresponding paths forms a path of length r-1, and their union forms either a cycle or a path of length k+1 in G. Let $P^k_r(G)$ be the k-iteration of r-path graph operator on a connected graph G. Let H be a subgraph of $P^k_r(G)$. The k-history $P^{-k}_r(H)$ is a subgraph of G that is induced by all edges that take part in the recursive definition of H. We present some general properties of k-histories and give a complete characterization of graphs that are k-histories of vertices of 2-path graph operator.

2

Connectivity of path graphs

63%

Knor M., Niepel L. u.

Discussiones Mathematicae Graph Theory

|

2000

|

tom 20

|

nr 2

181-195

EN

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.

3

Radii and centers in iterated line digraphs

63%

Knor M., Niepel L. u.

Discussiones Mathematicae Graph Theory

|

1996

|

tom 16

|

nr 1

17-26

EN

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.

Ograniczanie wyników

3 Discussiones Mathematicae Graph Theory

2 Knor M.

2 Niepel L. u.

1 Niepel L.

1 2007

1 2000

1 1996

Histories in path graphs

Connectivity of path graphs

Radii and centers in iterated line digraphs