Secure domination critical graphs

DOI10.1016/j.disc.2008.05.050zbMath1189.05126OpenAlexW2005291561MaRDI QIDQ1045117

P. J. P. Grobler, Christina M. Mynhardt

Publication date: 15 December 2009

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

Full work available at URL: https://doi.org/10.1016/j.disc.2008.05.050

zbMATH Keywords

secure dominationedge-removal-critical graphER-critical graphprotection of a graph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (15)

Secure domination in proper interval graphs ⋮ Exact algorithms for weak Roman domination ⋮ On the secure domination numbers of maximal outerplanar graphs ⋮ Global secure sets of grid-like graphs ⋮ On computing a minimum secure dominating set in block graphs ⋮ The complexity of secure domination problem in graphs ⋮ Unnamed Item ⋮ A linear algorithm for secure domination in trees ⋮ A characterization of trees with equal independent domination and secure domination numbers ⋮ Edge criticality in secure graph domination ⋮ The cost of edge removal in graph domination ⋮ Eternal and Secure Domination in Graphs ⋮ SECURE DOMINATING SETS IN THE LEXICOGRAPHIC PRODUCT OF GRAPHS ⋮ On minimum secure dominating sets of graphs ⋮ On secure domination in trees

Cites Work

• Irredundance, secure domination and maximum degree in trees
• Defending the Roman Empire from multiple attacks
• Roman domination in graphs.
• Defending the Roman Empire---a new strategy
• Secure domination and secure total domination in graphs
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