| Title:
|
Location-domatic number of a graph (English) |
| Author:
|
Zelinka, Bohdan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
123 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
67-71 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called locating-dominating, if for each $x\in V(G)-D$ there exists a vertex $y\to D$ adjacent to $x$ and for any two distinct vertices $x_1$, $x_2$ of $V(G)-D$ the intersections of $D$ with the neighbourhoods of $x_1$ and $x_2$ are distinct. The maximum number of classes of a partition of $V(G)$ whose classes are locating-dominating sets in $G$ is called the location-domatic number of $G.$ Its basic properties are studied. (English) |
| Keyword:
|
locating-dominating set |
| Keyword:
|
location-domatic partition |
| Keyword:
|
location-domatic number |
| Keyword:
|
domatic number |
| MSC:
|
05C35 |
| idZBL:
|
Zbl 0898.05034 |
| idMR:
|
MR1618719 |
| DOI:
|
10.21136/MB.1998.126298 |
| . |
| Date available:
|
2009-09-24T21:29:18Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126298 |
| . |
| Reference:
|
[1] E. J. Cockayne S. T. Hedetniemi: Towards a theory of domination in graphs.Networks 7 (1977), 247-261. MR 0483788, 10.1002/net.3230070305 |
| Reference:
|
[2] D. F. Rall P. J. Slater: On location-domination numbers for certain classes of graphs.Congressus Numerantium 45 (1984), 77-106. MR 0777715 |
| . |
