Location-domatic number of a graph
Bohdan Zelinka · Mathematica Bohemica · 1998
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.