# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# On domination in regular digraphs and in their reverse

Presented by Dr. Štefan GYüRKI
Type: Oral presentation
Track: General session

## Content

Let $D$ be a $k$-regular digraph and let $D^-$ be obtained by reversing all the arcs of $D$. We prove that the difference $f(D)-f(D^-)$ can be arbitrarily large if $k=2$ and $f$ is the domination number, or if $f$ is the total domination number and $k=3$. On the other hand, we show that $f(D)=f(D^-)$, if $k=2$ and $f$ is the total domination number. These statements complete the results of~\cite{nk}. \bibitem{nk} L. Niepel, M. Knor: \emph{Domination in a digraph and in its reverse}, Disc. Appl. Math., {\bf 157}(2009), 2973--2977.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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