Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Core of a Unicyclic Graph   A set S is independent in a graph G if no two vertices from S are adjacent.
By core(G) we mean the intersection of all maximum independent sets. The
independence number alpha(G) is the cardinality of a maximum independent set,
while mu(G) is the size of a maximum matching in G. A connected graph having
only one cycle, say C, is a unicyclic graph. In this paper we prove that if G
is a unicyclic graph of order n and n-1 = alpha(G) + mu(G), then core(G)
coincides with the union of cores of all trees in G-C.

16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg