| Title:
|
On strong digraphs with a prescribed ultracenter (English) |
| Author:
|
Chartrand, Gary |
| Author:
|
Gavlas, Heather |
| Author:
|
Schulz, Kelly |
| Author:
|
Winters, Steve J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
83-94 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| MSC:
|
05C12 |
| MSC:
|
05C20 |
| idZBL:
|
Zbl 0897.05033 |
| idMR:
|
MR1435607 |
| . |
| Date available:
|
2009-09-24T10:02:40Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127340 |
| . |
| Reference:
|
[1] G. Chartrand, K. Novotny, and S.J. Winters: The ultracenter and central fringe of a graph.Networks (to appear). MR 1844442 |
| Reference:
|
[2] G. Chartrand, G.L. Johns, and S. Tian: Directed distance in digraphs: centers and peripheries.Congr. Numer. 89 (1992), 89–95. MR 1208943 |
| Reference:
|
[3] M.P. Shaikh: On digraphs with prescribed centers and peripheries.J. Undergrad. Math. 25 (1993), 31–42. |
| Reference:
|
[4] S.J. Winters: Distance Associated with Subgraphs and Subdigraphs.Ph.D. Dissertation, Western Michigan University, 1993. |
| . |
