Geodesic
Location-domatic number of a graph
Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 67-71.

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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 
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Zelinka, Bohdan. Location-domatic number of a graph. Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 67-71. doi : 10.21136/MB.1998.126298. http://geodesic.mathdoc.fr/articles/10.21136/MB.1998.126298/

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