We investigate the domination number and total domination number of the graph K q (n; k) whose vertices are all the k-subspaces of an n-dimensional vector space over a eld with q elements and whose edges are the pairs fU; Wg of vertices such that U \ W = f0g. Bounds are obtained in general and exact results are obtained for n k 2 +k?1 and in other cases when q is suuciently large relative to n ...

Using hypergraph transversals it is proved that γt(Qn+1) = 2γ(Qn), where γt(G) and γ(G) denote the total domination number and the domination number of G, respectively, and Qn is the n-dimensional hypercube. More generally, it is shown that if G is a bipartite graph, then γt(G K2) = 2γ(G). Further, we show that the bipartiteness condition is essential by constructing, for any k > 1, a (non-bipa...

For a fixed positive integer k, a k-tuple total dominating set of a graph G is a subset D ⊆ V (G) such that every vertex of G is adjacent to at least k vertices in D. The k-tuple total domination problem is to determine a minimum k-tuple total dominating set of G. This paper studies k-tuple total domination from an algorithmic point of view. In particular, we present a linear-time algorithm for...