Sierpinski graph

Sierpinski graph - граф Серпинского.

The Sierpinski graph [math]\displaystyle{ S(n,k) }[/math] ([math]\displaystyle{ n,k \geq 1 }[/math]) is defined on the vertex set [math]\displaystyle{ \{0, 1, \ldots, n\}^{n} }[/math] , two different vertices [math]\displaystyle{ u = (i_{1}, i_{2}, \ldots, i_{n}) }[/math] and [math]\displaystyle{ v = (j_{1}, j_{2}, \ldots, j_{n}) }[/math] being adjacent if and only if [math]\displaystyle{ u \sim v }[/math]. The relation [math]\displaystyle{ \sim }[/math] is defined as follows: [math]\displaystyle{ u \sim v }[/math] if there exists an [math]\displaystyle{ h \in \{1, 2, \ldots, n\} }[/math] such that

(i) [math]\displaystyle{ \forall t, t\lt h \Rightarrow i_{t} = j_{t} }[/math],

(ii) [math]\displaystyle{ i_{h} \neq j_{h} }[/math],

(iii) [math]\displaystyle{ \forall t, t\gt h \Rightarrow i_{t} = j_{h} \& j_{t} = i_{h} }[/math].