Constructing Completely Independent Spanning Trees in a Family of Line-Graph-Based Data Center Networks

The past decade has seen growing importance being attached to the
Completely Independent Spanning Trees
(CISTs). The CISTs can facilitate many network functionalities, and the existence and construction schemes of CISTs in various networks can be an indicator of the network's robustness. In this paper, we establish the number of CISTs that can be constructed in the
line graph
of the complete graph
$K_n$
(denoted
$L(K_n)$
, for
$n\geq 4$
), and present an algorithm to construct the optimal (i.e., maximal) number of CISTs in
$L(K_n)$
. The
$L(K_n)$
is a special class of SWCube [13], an architectural model proposed for data center networks. Our construction algorithm is also implemented to verify its validity.