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Bounds for Domination Parameters in Cayley Graphs on Dihedral Group
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Open Journal of Discrete Mathematics·Volume 02 (2012)·Pages 5–10·Published 20 January 2012·DOI10.4236/ojdm.2012.21002
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Abstract
In this paper, sharp upper bounds for the domination number, total domination number and connected domination number for the Cayley graph G = Cay(D2n, Ω) constructed on the finite dihedral group D2n, and a specified generating set Ω of D2n. Further efficient dominating sets in G = Cay(D2n, Ω) are also obtained. More specifically, it is proved that some of the proper subgroups of D2n are efficient domination sets. Using this, an E-chain of Cayley graphs on the dihedral group is also constructed.
KeywordsCayley GraphDihedral GroupDominationTotal DominationConnected DominationEfficient Domination
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