Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An extremal problem: How small scale-free graph can be   The bloom of complex network study, in particular, with respect to scale-free
ones, is considerably triggering the research of scale-free graph itself.
Therefore, a great number of interesting results have been reported in the
past, including bounds of diameter. In this paper, we focus mainly on a problem
of how to analytically estimate the lower bound of diameter of scale-free
graph, i.e., how small scale-free graph can be. Unlike some pre-existing
methods for determining the lower bound of diameter, we make use of a
constructive manner in which one candidate model $\mathcal{G^*} (\mathcal{V^*},
\mathcal{E^*})$ with ultra-small diameter can be generated. In addition, with a
rigorous proof, we certainly demonstrate that the diameter of graph
$\mathcal{G^{*}}(\mathcal{V^{*}},\mathcal{E^{*}})$ must be the smallest in
comparison with that of any scale-free graph. This should be regarded as the
tight lower bound.

19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin