Opuscula Math. 32, no. 4 (2012), 751-760
http://dx.doi.org/10.7494/OpMath.2012.32.4.751

Opuscula Mathematica

False alarms in fault-tolerant dominating sets in graphs

Mateusz Nikodem

Abstract. We develop the problem of fault-tolerant dominating sets (liar's dominating sets) in graphs. Namely, we consider a new kind of fault - a false alarm. Characterization of such fault-tolerant dominating sets in three different cases (dependent on the classification of the types of the faults) are presented.

Keywords: liar's dominating set, fault-tolerant dominating set, false alarm, Hamming distance.

Mathematics Subject Classification: 05C69, 94B99.

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• Mateusz Nikodem
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
• Revised: 2012-05-15.
• Accepted: 2012-05-16.