The diameter of total domination vertex critical graphs

DOI10.1016/j.disc.2004.05.010zbMath1055.05113OpenAlexW1997029072MaRDI QIDQ1887647

Michael A. Henning, Teresa W. Haynes, Lucas C. Van Der Merwe, Wayne Goddard

Publication date: 22 November 2004

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

Full work available at URL: https://doi.org/10.1016/j.disc.2004.05.010

zbMATH Keywords

diametertotal dominationvertex critical

Mathematics Subject Classification ID

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

Related Items (27)

Total domination critical and stable graphs upon edge removal ⋮ Total domination stable graphs upon edge addition ⋮ Total domination dot-critical graphs ⋮ On the existence problem of the total domination vertex critical graphs ⋮ On 3-\(\gamma_t\)-vertex critical graphs of diameter three ⋮ Total domination stability in graphs ⋮ On the 2-rainbow domination stable graphs ⋮ Edge lifting and total domination in graphs ⋮ Perfect matchings in paired domination vertex critical graphs ⋮ On the Structure of Graphs Vertex Critical with Respect to Connected Domination ⋮ Total domination changing and stable graphs upon vertex removal ⋮ On \(4\)-\(\gamma_t\)-critical graphs of diameter two ⋮ The maximum diameter of total domination edge-critical graphs ⋮ Perfect matchings in total domination critical graphs ⋮ Properties of total domination edge-critical graphs ⋮ Matching properties in total domination vertex critical graphs ⋮ Total $k$-distance domination critical graphs ⋮ On the diameter of total domination vertex-critical graphs ⋮ On an open problem concerning total domination critical graphs ⋮ Diameters of uniform subset graphs ⋮ A survey of selected recent results on total domination in graphs ⋮ The existence problem of \(k\mathrm{-}\gamma_t\)-critical graphs ⋮ The diameter of paired-domination vertex critical graphs ⋮ A constructive characterization of total domination vertex critical graphs ⋮ Paired domination vertex critical graphs ⋮ On total domination vertex critical graphs of high connectivity ⋮ On the total domination critical graphs

Cites Work

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• Critical concepts in domination
• Hamiltonian properties of domination-critical graphs
• Vertex domination-critical graphs
• Total domination in graphs
• The diameter of domination k‐critical graphs
• Graphs with large total domination number
• Vertex domination‐critical graphs
• Domination critical graphs

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