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Domination in a digraph and in its reverse |
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| Authors: | L’udovít Niepel |
| Institution: | a Kuwait University, Faculty of Science, Department of Mathematics and Computer Science, P.O. box 5969, Safat 13060, Kuwait b Slovak University of Technology, Faculty of Civil Engineering, Department of Mathematics, Radlinského 11, 813 68 Bratislava, Slovakia |
| Abstract: | Let D be a digraph. By γ(D) we denote the domintaion number of D and by D− we denote a digraph obtained by reversing all the arcs of D. In this paper we prove that for every δ≥3 and k≥1 there exists a simple strongly connected δ-regular digraph Dδ,k such that  . Analogous theorem is obtained for total domination number provided that δ≥4. |
| Keywords: | Domination number Total domination number Directed graph Reverse digraph Converse |
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