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Displaying similar documents to “On Separating Sets of Edges in Contraction-Critical Graphs.”

Total domination edge critical graphs with maximum diameter

Lucas C. van der Merwe, Cristine M. Mynhardt, Teresa W. Haynes (2001)

Discussiones Mathematicae Graph Theory

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Denote the total domination number of a graph G by γₜ(G). A graph G is said to be total domination edge critical, or simply γₜ-critical, if γₜ(G+e) < γₜ(G) for each edge e ∈ E(G̅). For 3ₜ-critical graphs G, that is, γₜ-critical graphs with γₜ(G) = 3, the diameter of G is either 2 or 3. We characterise the 3ₜ-critical graphs G with diam G = 3.