Total Domination Edge Critical Graphs with Minimum Diameter.
Lucas C. van der Merwe, Christina M. Mynhardt, Teresa W. Haynes · Digital Commons - East Tennessee State University (East Tennessee State University) · 2003
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(Ḡ). For 3 t-critical graphs G, that is, γt-critical graphs with γt(G) = 3, the diameter of G is either 2 or 3. We study the 3t-critical graphs G with diam G = 2.