5 research outputs found
The generalized 4-connectivity of burnt pancake graphs
The generalized -connectivity of a graph , denoted by , is
the minimum number of internally edge disjoint -trees for any and . The generalized -connectivity is a natural extension of
the classical connectivity and plays a key role in applications related to the
modern interconnection networks. An -dimensional burnt pancake graph
is a Cayley graph which posses many desirable properties. In this paper, we try
to evaluate the reliability of by investigating its generalized
4-connectivity. By introducing the notation of inclusive tree and by studying
structural properties of , we show that for , that is, for any four vertices in , there exist () internally
edge disjoint trees connecting them in
Packing internally disjoint Steiner paths of data center networks
Let and denote the maximum number of
edge-disjoint paths in a graph such that
for any and . If
, then is the maximum number of edge-disjoint spanning
paths in . It is proved [Graphs Combin., 37 (2021) 2521-2533] that deciding
whether is NP-complete for a given . For an
integer with , the -path connectivity of a graph is
defined as min and , which
is a generalization of tree connectivity. In this paper, we study the -path
connectivity of the -dimensional data center network with -port switches
which has significate role in the cloud computing, and prove that
with and