Dominating sets in Cayley graphs on $ Z_{n} $

Main Article Content

T. Tamizh Chelvam
I. Rani

Abstract

A Cayley graph is a graph constructed out of a group $ \Gamma $ and its generating set $ A $. In this paper we attempt to find dominating sets in Cayley graphs constructed out of $ Z_{n} $. Actually we find the value of domination number for $ Cay(Z_{n}, A) $ and a minimal dominating set when $ |A| $ is even and further we have proved that $ Cay(Z_{n}, A) $ is excellent. We have also shown that $ Cay(Z_{n}, A) $ is $ 2- $excellent, when $ n = t(|A|+1)+1 $ for some integer $ t, t>0 $.

Article Details

How to Cite
Chelvam, T. T., & Rani, I. (2007). Dominating sets in Cayley graphs on $ Z_{n} $. Tamkang Journal of Mathematics, 38(4), 341–345. https://doi.org/10.5556/j.tkjm.38.2007.68
Section
Papers
Author Biographies

T. Tamizh Chelvam

Department of Mathematics, Manonmaniam Sundaranar University Tirunelveli 627 012 Tamil Nadu, India.

I. Rani

Department of Mathematics, Manonmaniam Sundaranar University Tirunelveli 627 012, Tamil Nadu, India.