  A graph with at most two vertices of the same degree is called antiregular
(Merris 2003), maximally nonregular (Zykov 1990) or quasiperfect (Behzad,
Chartrand 1967). If s_{k} is the number of independent sets of cardinality k in
a graph G, then I(G;x) = s_{0} + s_{1}x + ... + s_{alpha}x^{alpha} is the
independence polynomial of G (Gutman, Harary 1983), where alpha = alpha(G) is
the size of a maximum independent set. In this paper we derive closed formulae
for the independence polynomials of antiregular graphs. In particular, we
deduce that every antiregular graph A is uniquely defined by its independence
polynomial I(A;x), within the family of threshold graphs. Moreover, I(A;x) is
logconcave with at most two real roots, and I(A;-1) belongs to {-1,0}.
