Open AccessDominating 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 $