Independence polynomial

Independence polynomial --- многочлен независимости.

For a graph [math]\displaystyle{ G }[/math] with independence number [math]\displaystyle{ \beta }[/math], let [math]\displaystyle{ i_{k} }[/math] denote the number of independent sets of vertices of cardinality [math]\displaystyle{ k }[/math] in [math]\displaystyle{ G }[/math] ([math]\displaystyle{ k = 0,1, \ldots, \beta }[/math]). The independence polynomial of [math]\displaystyle{ G }[/math],

[math]\displaystyle{ i(G,x) = \sum_{k=0}^{\beta} i_{k}x^{k}, }[/math]

is the generating polinomial for the independence sequence [math]\displaystyle{ (i_{1}, i_{2}, \ldots, i_{\beta}). }[/math]