We determine upper bounds for $\gamma \left(Q{n}^t\right)$ and $i\left(Q{ₙ}^t\right)$, the domination and independent domination numbers, respectively, of the graph $Q{ₙ}^t$ obtained from the moves of queens on the n×n chessboard drawn on the torus.

For a graph property $𝒫$ and a graph $G$, we define the domination subdivision number with respect to the property $𝒫$ to be the minimum number of edges that must be subdivided (where each edge in $G$ can be subdivided at most once) in order to change the domination number with respect to the property $𝒫$. In this paper we obtain upper bounds in terms of maximum degree and orientable/non-orientable genus for the domination subdivision number with respect to an induced-hereditary property, total domination...

Let G be a graph with vertex set V (G), and let f : V (G) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and Σx∈N(v) f(x) ≥ k for each v ∈ V (G), where N(v) is the neighborhood of v, then f is a signed total k-dominating function on G. A set {f1, f2, . . . , fd} of distinct signed total k-dominating functions on G with the property that Σdi=1 fi(x) ≤ k for each x ∈ V (G), is called a signed total (k, k)-dominating family (of functions) on G. The maximum number of functions in a signed...