TITLE:
Bounds for Domination Parameters in Cayley Graphs on Dihedral Group
AUTHORS:
T. Tamizh Chelvam, G. Kalaimurugan
KEYWORDS:
Cayley Graph; Dihedral Group; Domination; Total Domination; Connected Domination; Efficient Domination
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.2 No.1,
January
20,
2012
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.