Monotonicity and expansion of global secure sets

Monotonicity and expansion of global secure sets

In this paper we investigate two problems, namely finding a global secure set of fixed cardinality and its expansion. For a given graph G=(V,E), a global secure set SD⊆V is a dominating set such that for every subset X⊆SD, |N[X]∩SD|≥|N[X]−SD|. Moreover, we say that a global secure set SD⊂V is expand...

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Veröffentlicht in:Discrete mathematics 2012-12, Vol.312 (23), p.3451-3456
1. Verfasser: Jesse-Józefczyk, Katarzyna
Format: Artikel
Sprache:eng
Schlagworte:
Co-quasi-threshold graph
Dominating set
Graphs
k-trees
Mathematical analysis
Secure set
Weakly quasi-threshold graph
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Zusammenfassung:In this paper we investigate two problems, namely finding a global secure set of fixed cardinality and its expansion. For a given graph G=(V,E), a global secure set SD⊆V is a dominating set such that for every subset X⊆SD, |N[X]∩SD|≥|N[X]−SD|. Moreover, we say that a global secure set SD⊂V is expandable if there exists a vertex v∈(V−SD) such that a set SD′=SD∪{v} is a global secure set.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2012.03.022