The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks

A set of the spanning trees in a graph
$G$
is called independent spanning trees if they have a common root
$r$
and for each vertex
$v\in V(G)\setminus \{r\}$
, the paths from
$v$
to
$r$
in any two trees are directed edge-disjoint and internally vertex-disjoint. The construction of independent spanning trees has many practical applications in reliable communication networks, such as fault-tolerant transmission and secure message distribution. A burnt pancake network
$BP_{n}$
is a kind of Cayley graph, which has been proposed as the topology of an interconnection network. In this paper, we provide a two stages construction scheme that can be used to construct a maximal number of independent spanning trees on a burnt pancake network in
$O(N\times n)$
time, where
$N$
is the number of nodes of
$BP_{n}$
and
$n$
is the dimension of the network. Furthermore, we prove the correctness of our proposed algorithm in constructing independent spanning trees.