Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Independent sets in chain cacti   In this paper chain cacti are considered. First, for two specific classes of
chain cacti (orto-chains and meta-chains of cycles with h vertices) the
recurrence relation for independence polynomial is derived. That recurrence
relation is then used in deriving explicit expressions for independence number
and number of maximum independent sets for such chains. Also, the recurrence
relation for total number of independent sets for such graphs is derived.
Finaly, the proof is provided that orto-chains and meta-chains are the only
extremal chain cacti with respect to total number of independent sets
(orto-chains minimal and meta-chains maximal).

22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
3
The categories of this paper are: physics