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Irredundant and perfect neighbourhood sets in trees

โœ Scribed by E.J. Cockayne; S.M. Hedetniemi; S.T. Hedetniemi; C.M. Mynhardt


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
373 KB
Volume
188
Category
Article
ISSN
0012-365X

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โœฆ Synopsis


For any tree T, it is proved that 0(T), the smallest cardinality of a perfect neighbourhood set, is bounded above by ir(T), the smallest cardinality of a maximal irredundant set.


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## Abstract In this paper, we show that a Cayley graph for an abelian group has an independent perfect domination set if and only if it is a covering graph of a complete graph. As an application, we show that the hypercube __Q~n~__ has an independent perfect domination set if and only if __Q~n~__ i