Realizability of the total domination criticality index
For a graph G = (V, E), a set S ⊆ V is a total dominating set if every vertex in V is adjacent to some vertex in S. The smallest cardinality of any total dominating set is the total domination number γt(G). For an arbitrary edge e εE(Ḡ), γt(G) - 2 ≤ γt(G + e) ≤ γt(G); if the latter inequality is strict for each e ε E(Ḡ) ≠ φ, then G is said to be γt-critical. The criticality index of an edge e ε E(Ḡ) is γt(e) = γt(G) - γt(G + e). Let E(Ḡ) = [e1...,em