On the out-domination and in-domination numbers of a digraph
Discrete Mathematics
Extended Dominating-Set-Based Routing in Ad Hoc Wireless Networks with Unidirectional Links
IEEE Transactions on Parallel and Distributed Systems
Note: Domination in a digraph and in its reverse
Discrete Applied Mathematics
Approximately dominating representatives
ICDT'05 Proceedings of the 10th international conference on Database Theory
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For a digraph D, the domination number of D is denoted by @c(D), the total domination number of D is denoted by @c"t(D), and the digraph obtained by reversing all the arcs of D is denoted by D^-. We show that the difference @c(D^-)-@c(D) can be arbitrarily large in the class of 2-regular strongly connected digraphs, and similarly, @c"t(D^-)-@c"t(D) can be arbitrarily large in the class of 3-regular strongly connected digraphs. Similar results for larger valencies were proved in Niepel and Knor (2009) [5]. We also show that every 2-regular digraph D satisfies @c"t(D)=@c"t(D^-). Altogether this solves problems 1 and 2 posed in [5].