Geodesic
Total domination edge critical graphs with maximum diameter
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 2, pp. 187-205.

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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. 
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van der Merwe, Lucas; Mynhardt, Cristine; Haynes, Teresa. Total domination edge critical graphs with maximum diameter. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 2, pp. 187-205. http://geodesic.mathdoc.fr/item/DMGT_2001_21_2_a4/

[1] E. Cockayne, R. Dawes and S. Hedetniemi, Total domination in graphs, Networks 10 (1980) 211-219, doi: 10.1002/net.3230100304.

[2] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, 1998).

[3] T.W. Haynes, C.M. Mynhardt and L.C. van der Merwe, Total domination edge critical graphs, Utilitas Math. 54 (1998) 229-240.

[4] T.W. Haynes, C.M. Mynhardt and L.C. van der Merwe, Criticality index of total domination, Congr. Numer. 131 (1998) 67-73.

[5] D.P. Sumner and P. Blitch, Domination critical graphs, J. Combin. Theory (B) 34 (1983) 65-76, doi: 10.1016/0095-8956(83)90007-2.

[6] D.P. Sumner and E. Wojcicka, Graphs critical with respect to the domination number, Domination in Graphs: Advanced Topics (Chapter 16), T.W. Haynes, S.T. Hedetniemi and P.J. Slater, eds. (Marcel Dekker, Inc., New York, 1998).