Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On graphs having maximal independent sets of exactly $t$ distinct
  cardinalities   For a given positive integer t we consider graphs having maximal independent
sets of precisely t distinct cardinalities and restrict our attention to those
that have no vertices of degree one. In the situation when t is four or larger
and the length of the shortest cycle is at least 6t-6, we completely
characterize such graphs.

14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph