Bounds for Domination Parameters in Cayley Graphs on Dihedral Group

• 作者: G. Kalaimurugan T. Tamizh Chelvam
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: CAYLEY GRAPH Dihedral Group DOMINATION TOTAL DOMINATION CONNECTED DOMINATION Efficient DOMINATION
• 年，卷（期）: 2012,（1）
• 页码范围: 5-10
• 页数: 6页
• 分类号: O1

摘要

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.