Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Edge-Szeged Index and the PI Index of Benzenoid Systems in Linear
  Time   The edge-Szeged index of a graph $G$ is defined as $Sz_e(G) = \sum_{e=uv \in
E(G)}m_u(e)m_v(e)$, where $m_u(e)$ denotes the number of edges of $G$ whose
distance to $u$ is smaller than the distance to $v$ and $m_v(e)$ denotes the
number of edges of $G$ whose distance to $v$ is smaller than the distance to
$u$. Similarly, the PI index is defined as $PI(G) = \sum_{e=uv \in E(G)}(m_u(e)
+ m_v(e))$. In this paper it is shown how the problem of calculating the
indices of a benzenoid system can be reduced to the problem of calculating
weighted indices of three different weighted quotient trees. Furthermore, using
these results, algorithms are established that, for a given benzenoid system
$G$ with $m$ edges, compute the edge-Szeged index and the PI index of $G$ in
$O(m)$ time. Moreover, it is shown that the results can also be applied to
weighted benzenoid systems.

36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga