  An independent set in a graph is a set of pairwise non-adjacent vertices, and
a(G) is the size of a maximum independent set in the graph G. If s_{k} is the
number of independent sets of cardinality k in G, then
I(G;x)=s_0+s_1*x+s_2*x^2+...+s_a*x^a,a=a(G), is called the independence
polynomial of G (I. Gutman and F. Harary, 1983). If s_{a-i}=f(i)*s_{i} holds
for every i, then I(G;x) is called f-symmetric (f-palindromic). If f(i)=1, then
I(G;x) is symmetric (palindromic). The corona of the graphs G and H is the
graph G*H obtained by joining each vertex of G to all the vertices of a copy of
H. In this paper we show that if H is a graph with p vertices, q edges, and
alpha(H)=2, then I(G*H;x) is f-symmetric for some elegant function f. In
particular, if H = K_{r}-e, we show that I(G*H;x) is symmetric and unimodal,
with a unique mode. This finding generalizes results due to (Stevanovic, 1998)
and (Mandrescu, 2012) claiming that I(G*(K_2-e);x)=I(G*2K_1;x) is symmetric and
unimodal for every graph G.
