On a graph's security number

DOI10.1016/j.disc.2009.02.005zbMath1205.05166OpenAlexW2088547121MaRDI QIDQ1043972

Ronald D. Dutton

Publication date: 10 December 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2009.02.005

zbMATH Keywords

attackdefensealliancessecure sets

Mathematics Subject Classification ID

Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (15)

The security number of strong grid-like graphs ⋮ Global edge alliances in graphs ⋮ Secure domination of honeycomb networks ⋮ Global security in claw-free cubic graphs ⋮ Secure sets and their expansion in cubic graphs ⋮ Secure domination of some graph operators ⋮ Security in Sierpiński graphs ⋮ Global secure sets of grid-like graphs ⋮ New solutions for slow moving kinks in a forced Frenkel-Kontorova chain ⋮ The security number of lexicographic products ⋮ Alliances in graphs: parameters, properties and applications -- a survey ⋮ On the security number of the Cartesian product of graphs ⋮ Monotonicity and expansion of global secure sets ⋮ Metastability and dynamics of discrete topological singularities in two dimensions: a \(\Gamma\)-convergence approach ⋮ The possible cardinalities of global secure sets in cographs

Cites Work

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• Unfriendly partitions of a graph
• Powerful alliances in graphs
• Global defensive alliances in graphs
• Security in graphs
• Bounds on a graph's security number
• Offensive alliances in graphs

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