ABSTRACT
An absorbant of a digraph D is a set such that, for every , there exists an arc with . An absorbant S is efficient if no two vertices in S have a common in-neighbour and the subdigraph induced by S has no arc. The efficient absorbant conjecture in generalized De Bruijn digraphs is as follows: There exists an efficient absorbant in generalized De Bruijn digraph with if and only if c is a multiple of . In this paper, we show that the sufficient condition of the efficient absorbant conjecture in generalized De Bruijn digraphs is affirmative.
2010 AMS SUBJECT CLASSIFICATION:
Acknowledgments
The authors would like to thank anonymous referees for their careful reading with corrections and useful comments which helped to improve the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.