Bounds for Domination Parameters in Cayley Graphs on Dihedral Group

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DOI: 10.4236/ojdm.2012.21002   PDF   HTML   XML   4,192 Downloads   9,944 Views   Citations

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.

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T. Chelvam and G. Kalaimurugan, "Bounds for Domination Parameters in Cayley Graphs on Dihedral Group," Open Journal of Discrete Mathematics, Vol. 2 No. 1, 2012, pp. 5-10. doi: 10.4236/ojdm.2012.21002.

Conflicts of Interest

The authors declare no conflicts of interest.

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