Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the independence polynomial of an antiregular graph   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}.

9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol