Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fibonacci Identities and Graph Colorings   We generalize both the Fibonacci and Lucas numbers to the context of graph
colorings, and prove some identities involving these numbers. As a corollary we
obtain new proofs of some known identities involving Fibonacci numbers such as
\[F_{r+s+t} = F_{r+1}F_{s+1}F_{t+1} + F_r F_s F_t - F_{r-1}F_{s-1}F_{t-1}.\]

11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con