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

T. Tamizh Chelvam | Zendy; Indu Rani | Zendy

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

Author(s) -

T. Tamizh Chelvam,

Indu Rani

Publication year - 2007

Publication title -

tamkang journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.324

H-Index - 18

eISSN - 0049-2930

pISSN - 2073-9826

DOI - 10.5556/j.tkjm.38.2007.68

Subject(s) - cayley graph , mathematics , combinatorics , graph , dominating set , integer (computer science) , discrete mathematics , set (abstract data type) , computer science , vertex (graph theory) , programming language

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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