The domination number of wrapped butterfly digraphs

Juan Liu, Xindong Zhang and Xing Chen

Applied Mathematics and Computation, 2021, vol. 409, issue C

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.

Keywords: Butterfly digraph; Wrapped butterfly digraph; Dominating set; Domination number (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321004963

DOI: 10.1016/j.amc.2021.126407

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