Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Measures of Edge Fault Tolerance in (n,k)-star Graphs   This paper considers a kind of generalized measure $\lambda_s^{(h)}$ of fault
tolerance in the $(n,k)$-star graph $S_{n,k}$ for $2\leqslant k \leqslant n-1$
and $0\leqslant h \leqslant n-k$, and determines
$\lambda_s^{(h)}(S_{n,k})=\min\{(n-h-1)(h+1), (n-k+1)(k-1)\}$, which implies
that at least $\min\{(n-k+1)(k-1),(n-h-1)(h+1)\}$ edges of $S_{n,k}$ have to
remove to get a disconnected graph that contains no vertices of degree less
than $h$. This result shows that the $(n,k)$-star graph is robust when it is
used to model the topological structure of a large-scale parallel processing
system.

19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph