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T. Tamizh Chelvam and I. Rani, “Total and Connected Domination Numbers of Cayley Graphs on Zn,” Advanced Studies in Contemporary Mathematics, Vol. 20, 2010, pp. 57-61.

has been cited by the following article:

• 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.