Domination sequences. (Q2715967)

Let \(I(G)\) be a numerical invariant of a graph \(G\). A sequence \(a_1,a_2,\dots ,a_n\) may be considered such that the sequence of graphs \(G_1,G_2,\dots ,G_n\) exists and \(G_i\) has \(i\) vertices, \(G_i\) is an induced subgraph of \(G_{i+1}\) and \(I(G_i)=a_i\). Such sequences are considered for various choices of \(I(G)\). They are the domination number, independent domination number, connected domination number, total domination number, chromatic number, etc.