Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Measures of Fault Tolerance in Exchanged Hypercubes   The exchanged hypercube $EH(s,t)$, proposed by Loh {\it et al.} [The
exchanged hypercube, IEEE Transactions on Parallel and Distributed Systems 16
(9) (2005) 866-874], is obtained by removing edges from a hypercube
$Q_{s+t+1}$. This paper considers a kind of generalized measures $\kappa^{(h)}$
and $\lambda^{(h)}$ of fault tolerance in $EH(s,t)$ with $1\leqslant s\leqslant
t$ and determines $\kappa^{(h)}(EH(s,t))=\lambda^{(h)}(EH(s,t))= 2^h(s+1-h)$
for any $h$ with $0\leqslant h\leqslant s$. The results show that at least
$2^h(s+1-h)$ vertices (resp. $2^h(s+1-h)$ edges) of $EH(s,t)$ have to be
removed to get a disconnected graph that contains no vertices of degree less
than $h$, and generalizes some known results.

5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat