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

Authors

  • T. Tamizh Chelvam
  • I. Rani

DOI:

https://doi.org/10.5556/j.tkjm.38.2007.68

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 $.

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.

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Published

2007-12-31

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

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Section

Papers