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Irredundance and Maximum Degree in Graphs

Published online by Cambridge University Press:  01 June 1997

E. J. COCKAYNE
Affiliation:
University of Victoria, BC, Canada
C. M. MYNHARDT
Affiliation:
Department of Mathematics, University of South Africa, P. O. Box 392, Pretoria 0001, South Africa (e-mail: mynhacm@alpha.unisa.ac.za)

Abstract

It is proved that the smallest cardinality among the maximal irredundant sets in an n–vertex graph with maximum degree Δ([ges ]2) is at least 2n/3Δ. This substantially improves a bound by Bollobás and Cockayne [1]. The class of graphs which attain this bound is characterised.

Type
Research Article
Copyright
1997 Cambridge University Press

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