Article citationsMore>>

R J. Huang and J.-M. Xu, “The Bondage and Efficient Domination of Vertex Transitive Graphs,” Discrete Mathe- matics, Vol. 308, No. 4, 2008, pp. 571-582. doi:10.1016/j.disc.2007.03.027

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.