On strong digraphs with a prescribed ultracenter
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 1, pp. 83-94
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library
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 $\mathop {\mathrm rad}\nolimits D$ and the subdigraph induced by the central vertices is the center $C(D)$. For a central vertex $v$ in a strong digraph $D$ with $\mathop {\mathrm rad}\nolimits D\text{diam} D$, 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.
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 $\mathop {\mathrm rad}\nolimits D$ and the subdigraph induced by the central vertices is the center $C(D)$. For a central vertex $v$ in a strong digraph $D$ with $\mathop {\mathrm rad}\nolimits D\text{diam} D$, 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.
@article{CMJ_1997_47_1_a5,
author = {Chartrand, Gary and Gavlas, Heather and Schulz, Kelly and Winters, Steve J.},
title = {On strong digraphs with a prescribed ultracenter},
journal = {Czechoslovak Mathematical Journal},
pages = {83--94},
year = {1997},
volume = {47},
number = {1},
mrnumber = {1435607},
zbl = {0897.05033},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_1997_47_1_a5/}
}
TY - JOUR AU - Chartrand, Gary AU - Gavlas, Heather AU - Schulz, Kelly AU - Winters, Steve J. TI - On strong digraphs with a prescribed ultracenter JO - Czechoslovak Mathematical Journal PY - 1997 SP - 83 EP - 94 VL - 47 IS - 1 UR - http://geodesic.mathdoc.fr/item/CMJ_1997_47_1_a5/ LA - en ID - CMJ_1997_47_1_a5 ER -
Chartrand, Gary; Gavlas, Heather; Schulz, Kelly; Winters, Steve J. On strong digraphs with a prescribed ultracenter. Czechoslovak Mathematical Journal, Tome 47 (1997) no. 1, pp. 83-94. http://geodesic.mathdoc.fr/item/CMJ_1997_47_1_a5/
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