Properties of total domination edge-critical graphs

DOI10.1016/j.dam.2009.09.004zbMath1226.05196OpenAlexW2078474714MaRDI QIDQ968121

Lucas C. Van Der Merwe, Michael A. Henning

Publication date: 5 May 2010

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

Full work available at URL: https://doi.org/10.1016/j.dam.2009.09.004

zbMATH Keywords

boundsdiametertotal dominationedge critical

Mathematics Subject Classification ID

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

Related Items (3)

Perfect matchings in total domination critical graphs ⋮ Total edge critical graphs with leaves ⋮ Hamiltonicity of \(3_t\)EC graphs with \(\alpha=\kappa +1\)

Cites Work

• Total domination of graphs and small transversals of hypergraphs
• On diameter 2-critical graphs
• On diameter critical graphs
• Hamiltonicity in 3-domination-critical graphs with \(\alpha= \delta+2\)
• Some properties of 3-domination-critical graphs
• The diameter of total domination vertex critical graphs
• On a conjecture of Murty and Simon on diameter 2-critical graphs
• Critical concepts in domination
• Bicritical domination
• Hamiltonian properties of domination-critical graphs
• Total domination in graphs
• The maximum number of edges in a minimal graph of diameter 2
• The diameter of domination k‐critical graphs
• Independence and hamiltonicity in 3-domination-critical graphs
• Total Domination Edge Critical Graphs with Maximum Diameter
• Domination critical graphs
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