The independence polynomial of rooted products of graphs Original Research Article

I(G;x)=∑k=0α(G)skxk=s0+s1x+s2x2+⋯+sα(G)xα(G)(s0≔1),We obtain a number of formulae expressing the independence polynomials of two sorts of the rooted product of graphs in terms of such polynomials of constituent graphs. In particular, it enables us to build infinite families of graphs whose independence polynomials have only real roots.