Bounds for Domination Parameters in Cayley Graphs on Dihedral Group

T. Tamizh Chelvam, G. Kalaimurugan

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DOI: 10.4236/ojdm.2012.21002                

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.

Keywords

Cayley Graph; Dihedral Group; Domination; Total Domination; Connected Domination; Efficient Domination

Conflicts of Interest

The authors declare no conflicts of interest.

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