On strong digraphs with a prescribed ultracenter

Chartrand, Gary, et al. "On strong digraphs with a prescribed ultracenter." Czechoslovak Mathematical Journal 47.1 (1997): 83-94. <http://eudml.org/doc/30348>.

@article{Chartrand1997,
abstract = {The (directed) distance from a vertex $u$ to a vertex $v$ in a strong digraph $D$ is the length of a shortest $u$-$v$ (directed) path in $D$. The eccentricity of a vertex $v$ of $D$ is the distance from $v$ to a vertex furthest from $v$ in $D$. The radius rad$D$ is the minimum eccentricity among the vertices of $D$ and the diameter diam$D$ is the maximum eccentricity. A central vertex is a vertex with eccentricity $\mathop \{\mathrm \{r\}ad\}\nolimits D$ and the subdigraph induced by the central vertices is the center $C(D)$. For a central vertex $v$ in a strong digraph $D$ with $\mathop \{\mathrm \{r\}ad\}\nolimits D<\text\{diam\} D$, the central distance $c(v)$ of $v$ is the greatest nonnegative integer $n$ such that whenever $d(v,x)\le n$, then $x$ is in $C(D)$. The maximum central distance among the central vertices of $D$ is the ultraradius urad$D$ and the subdigraph induced by the central vertices with central distance urad$D$ is the ultracenter $UC(D)$. For a given digraph $D$, the problem of determining a strong digraph $H$ with $UC(H)=D$ and $C(H)\ne D$ is studied. This problem is also considered for digraphs that are asymmetric.},
author = {Chartrand, Gary, Gavlas, Heather, Schultz, Kelly, Winters, Steven J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {ultraradius of a digraph; ultracenter of a digraph},
language = {eng},
number = {1},
pages = {83-94},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On strong digraphs with a prescribed ultracenter},
url = {http://eudml.org/doc/30348},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Chartrand, Gary
AU - Gavlas, Heather
AU - Schultz, Kelly
AU - Winters, Steven J.
TI - On strong digraphs with a prescribed ultracenter
JO - Czechoslovak Mathematical Journal
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 1
SP - 83
EP - 94
AB - The (directed) distance from a vertex $u$ to a vertex $v$ in a strong digraph $D$ is the length of a shortest $u$-$v$ (directed) path in $D$. The eccentricity of a vertex $v$ of $D$ is the distance from $v$ to a vertex furthest from $v$ in $D$. The radius rad$D$ is the minimum eccentricity among the vertices of $D$ and the diameter diam$D$ is the maximum eccentricity. A central vertex is a vertex with eccentricity $\mathop {\mathrm {r}ad}\nolimits D$ and the subdigraph induced by the central vertices is the center $C(D)$. For a central vertex $v$ in a strong digraph $D$ with $\mathop {\mathrm {r}ad}\nolimits D<\text{diam} D$, the central distance $c(v)$ of $v$ is the greatest nonnegative integer $n$ such that whenever $d(v,x)\le n$, then $x$ is in $C(D)$. The maximum central distance among the central vertices of $D$ is the ultraradius urad$D$ and the subdigraph induced by the central vertices with central distance urad$D$ is the ultracenter $UC(D)$. For a given digraph $D$, the problem of determining a strong digraph $H$ with $UC(H)=D$ and $C(H)\ne D$ is studied. This problem is also considered for digraphs that are asymmetric.
LA - eng
KW - ultraradius of a digraph; ultracenter of a digraph
UR - http://eudml.org/doc/30348
ER -