Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Further analysis on the total number of subtrees of trees   We study that over some types of trees with a given number of vertices, which
trees minimize or maximize the total number of subtrees. Trees minimizing
(resp. maximizing) the total number of subtrees usually maximize (resp.
minimize) the Wiener index, and vice versa. Here are some of our results: (1)
Let $\mathscr{T}_n^k$ be the set of all $n$-vertex trees with $k$ leaves, we
determine the maximum (resp. minimum) value of the total number of subtrees of
trees among $\mathscr{T}_n^k$ and characterize the extremal graphs. (2) Let
$\mathscr{P}_n^{p,q}$ be the set of all $n$-vertex trees, each of which has a
$(p,q)$-bipartition, we determine the maximum (resp. minimum) value of the
total number of subtrees of trees among $\mathscr{P}_n^{p,q}$ and characterize
the extremal graphs. (3) Let $\mathscr{A}_n^q$ be the set of all $q$-ary trees
with $n$ non-leaf vertices, we determine the minimum value of the total number
of subtrees of trees among $\mathscr{A}_n^q$ and identify the extremal graph.

21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph