Location-domatic number of a graph
Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 67-71
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MR Zbl
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.
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.
DOI :
10.21136/MB.1998.126298
Classification :
05C35
Keywords: locating-dominating set; location-domatic partition; location-domatic number; domatic number
Keywords: locating-dominating set; location-domatic partition; location-domatic number; domatic number
Zelinka, Bohdan. Location-domatic number of a graph. Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 67-71. doi: 10.21136/MB.1998.126298
@article{10_21136_MB_1998_126298,
author = {Zelinka, Bohdan},
title = {Location-domatic number of a graph},
journal = {Mathematica Bohemica},
pages = {67--71},
year = {1998},
volume = {123},
number = {1},
doi = {10.21136/MB.1998.126298},
mrnumber = {1618719},
zbl = {0898.05034},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1998.126298/}
}