On $k$-strong distance in strong digraphs

Zhang, Ping. "On $k$-strong distance in strong digraphs." Mathematica Bohemica 127.4 (2002): 557-570. <http://eudml.org/doc/249029>.

@article{Zhang2002,
abstract = {For a nonempty set $S$ of vertices in a strong digraph $D$, the strong distance $d(S)$ is the minimum size of a strong subdigraph of $D$ containing the vertices of $S$. If $S$ contains $k$ vertices, then $d(S)$ is referred to as the $k$-strong distance of $S$. For an integer $k \ge 2$ and a vertex $v$ of a strong digraph $D$, the $k$-strong eccentricity $\mathop \{\mathrm \{s\}e\}_k(v)$ of $v$ is the maximum $k$-strong distance $d(S)$ among all sets $S$ of $k$ vertices in $D$ containing $v$. The minimum $k$-strong eccentricity among the vertices of $D$ is its $k$-strong radius $\mathop \{\mathrm \{s\}rad\}_k D$ and the maximum $k$-strong eccentricity is its $k$-strong diameter $_k D$. The $k$-strong center ($k$-strong periphery) of $D$ is the subdigraph of $D$ induced by those vertices of $k$-strong eccentricity $\mathop \{\mathrm \{s\}rad\}_k(D)$ ($_k (D)$). It is shown that, for each integer $k \ge 2$, every oriented graph is the $k$-strong center of some strong oriented graph. A strong oriented graph $D$ is called strongly $k$-self-centered if $D$ is its own $k$-strong center. For every integer $r \ge 6$, there exist infinitely many strongly 3-self-centered oriented graphs of 3-strong radius $r$. The problem of determining those oriented graphs that are $k$-strong peripheries of strong oriented graphs is studied.},
author = {Zhang, Ping},
journal = {Mathematica Bohemica},
keywords = {strong distance; strong eccentricity; strong center; strong periphery; strong distance; strong eccentricity; strong center; strong periphery},
language = {eng},
number = {4},
pages = {557-570},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $k$-strong distance in strong digraphs},
url = {http://eudml.org/doc/249029},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Zhang, Ping
TI - On $k$-strong distance in strong digraphs
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 4
SP - 557
EP - 570
AB - For a nonempty set $S$ of vertices in a strong digraph $D$, the strong distance $d(S)$ is the minimum size of a strong subdigraph of $D$ containing the vertices of $S$. If $S$ contains $k$ vertices, then $d(S)$ is referred to as the $k$-strong distance of $S$. For an integer $k \ge 2$ and a vertex $v$ of a strong digraph $D$, the $k$-strong eccentricity $\mathop {\mathrm {s}e}_k(v)$ of $v$ is the maximum $k$-strong distance $d(S)$ among all sets $S$ of $k$ vertices in $D$ containing $v$. The minimum $k$-strong eccentricity among the vertices of $D$ is its $k$-strong radius $\mathop {\mathrm {s}rad}_k D$ and the maximum $k$-strong eccentricity is its $k$-strong diameter $_k D$. The $k$-strong center ($k$-strong periphery) of $D$ is the subdigraph of $D$ induced by those vertices of $k$-strong eccentricity $\mathop {\mathrm {s}rad}_k(D)$ ($_k (D)$). It is shown that, for each integer $k \ge 2$, every oriented graph is the $k$-strong center of some strong oriented graph. A strong oriented graph $D$ is called strongly $k$-self-centered if $D$ is its own $k$-strong center. For every integer $r \ge 6$, there exist infinitely many strongly 3-self-centered oriented graphs of 3-strong radius $r$. The problem of determining those oriented graphs that are $k$-strong peripheries of strong oriented graphs is studied.
LA - eng
KW - strong distance; strong eccentricity; strong center; strong periphery; strong distance; strong eccentricity; strong center; strong periphery
UR - http://eudml.org/doc/249029
ER -