### System-theoretic analysis of due-time performance in production systems.

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A set S of vertices of a graph G = (V,E) is a dominating set if every vertex of V-S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set of G, and the domination subdivision number $s{d}_{\gamma}\left(G\right)$ is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the domination number. Arumugam conjectured that $1\le s{d}_{\gamma}\left(G\right)\le 3$ for any graph G. We give a counterexample to this conjecture. On the other hand, we show...

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