Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Algebraic Connectivity and the Clique Number of Graphs   This paper investigates some relationship between the algebraic connectivity
and the clique number of graphs. We characterize all extremal graphs which have
the maximum and minimum the algebraic connectivity among all graphs of order
$n$ with the clique number $r$, respectively. In turn, an upper and lower
bounds for the clique number of a graph in terms of the algebraic connectivity
are obtained. Moreover, a spectral version of the Erd\H{o}s-Stone theorem in
terms of the algebraic connectivity of graphs is presented.

16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci