Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the average Steiner 3-eccentricity of trees   The Steiner $k$-eccentricity of a vertex $v$ of a graph $G$ is the maximum
Steiner distance over all $k$-subsets of $V(G)$ which contain $v$. In this
paper Steiner $3$-eccentricity is studied on trees. Some general properties of
the Steiner $3$-eccentricity of trees are given. A tree transformation which
does not increase the average Steiner $3$-eccentricity is given. As its
application, several lower and upper bounds for the average Steiner
$3$-eccentricity of trees are derived.

14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas