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