Security in Sierpiński graphs

A secure set S⊆V of a graph G=(V,E) is a set whose every nonempty subset can be successfully defended from an attack, under appropriate definitions of ‘attack’ and ‘defense’. The set S is secure when |N[X]⋂S|≥|N[X]−S| for every X⊆S. A set S⊆V is secure dominating if it is both secure and dominating....

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Bibliographic Details
Published in:Discrete Applied Mathematics 2023-03, Vol.328, p.10-15
Main Authors: Menon, Manju K., M.R., Chithra, K.S., Savitha
Format: Article
Language:English
Subjects:
Secure dominating sets
Secure sets
Sierpiński graphs
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Summary:A secure set S⊆V of a graph G=(V,E) is a set whose every nonempty subset can be successfully defended from an attack, under appropriate definitions of ‘attack’ and ‘defense’. The set S is secure when |N[X]⋂S|≥|N[X]−S| for every X⊆S. A set S⊆V is secure dominating if it is both secure and dominating. The minimum cardinality of a secure set in G is the security number of G, s(G), and the minimum cardinality of a secure-dominating set in G is the secure domination number of G,γs(G). In this paper, we initiate a study of these parameters in the well-known Sierpiński graphs.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2022.11.017