Abstract
Let D be a digraph and let γ(D) and γt(D) be domination number and total domination number of D, respectively. In this paper, we discuss the domination number of butterfly digraphs and wrapped butterfly digraphs, and give the exact values of total domination number of wrapped butterfly digraphs. We show that each of the following holds. (i)⌈ndnd+1⌉≤γ(WBF→(d,n))≤{ndn+1d+1,ifnisodd,ndn−1d+1+n2,ifniseven. (ii)γt(WBF→(d,n))=ndn−1.
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