Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scale-free tree network with an ultra-large diameter   Scale-free networks are prevalently observed in a great variety of complex
systems, which triggers various researches relevant to networked models of such
type. In this work, we propose a family of growth tree networks
$\mathcal{T}_{t}$, which turn out to be scale-free, in an iterative manner. As
opposed to most of published tree models with scale-free feature, our tree
networks have the power-law exponent $\gamma=1+\ln5/\ln2$ that is obviously
larger than $3$. At the same time, "small-world" property can not be found
particularly because models $\mathcal{T}_{t}$ have an ultra-large diameter
$D_{t}$, i.e., $D_{t}\sim|\mathcal{T}_{t}|^{\ln3/\ln5}$ where
$|\mathcal{T}_{t}|$ represents vertex number. In addition, we also study random
walks on tree networks $\mathcal{T}_{t}$ and derive exact solution to mean
hitting time $\langle\mathcal{H}_{t}\rangle$. The results suggest that analytic
formula for quantity $\langle\mathcal{H}_{t}\rangle$ as a function of vertex
number $\mathcal{T}_{t}$ has a power-law form, i.e.,
$\langle\mathcal{H}_{t}\rangle\sim|\mathcal{T}_{t}|^{1+\ln3/\ln5}$ , a
characteristic that is rarely encountered in the realm of scale-free tree
networks. Lastly, we execute extensive experimental simulations, and find that
empirical analysis is in strong agreement with theoretical results.

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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat