Substitutional closure

Substitutional closure --- подстановочное замыкание.

For a class [math]\displaystyle{ {\mathcal P} }[/math] of graphs, the substitutional closure [math]\displaystyle{ {\mathcal P}^{\ast} }[/math] consists of all graphs that can be obtained from [math]\displaystyle{ {\mathcal P} }[/math] by repeated substitutions; that is, [math]\displaystyle{ {\mathcal P}^{\ast} }[/math] is generated by the following rules:

(S1) [math]\displaystyle{ {\mathcal P} \subseteq {\mathcal P}^{\ast} }[/math], and

(S2) if [math]\displaystyle{ G,H \in{\mathcal P}^{\ast} }[/math] and [math]\displaystyle{ v \in V(G) }[/math], then [math]\displaystyle{ G(v \rightarrow H) \in {\mathcal P}^{\ast} }[/math].