Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Menger-type connectivity of line graphs of faulty hypercubes   A connected graph $G$ is called strongly Menger edge connected if $G$ has
min\{deg$_G(x)$, deg$_G(y)$\} edge-disjoint paths between any two distinct
vertices $x$ and $y$ in $G$. In this paper, we consider two types of strongly
Menger edge connectivity of the line graphs of $n$-dimensional hypercube-like
networks with faulty edges, namely the $m$-edge-fault-tolerant and
$m$-conditional edge-fault-tolerant strongly Menger edge connectivity. We show
that the line graph of any $n$-dimensional hypercube-like network is
$(2n-4)$-edge-fault-tolerant strongly Menger edge connected for $n\geq 3$ and
$(4n-10)$-conditional edge-fault-tolerant strongly Menger edge connected for
$n\geq 4$. The two bounds for the maximum number of faulty edges are best
possible.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat