The structure fault tolerance of burnt pancake networks

One of the symbolic parameters to measure the fault tolerance of a network is its connectivity. The H H -structure connectivity and H H -substructure connectivity extend the classical connectivity and are more practical. For a graph G G and its connected subgraph H H , the H H -structure connectivity κ ( G ; H ) \kappa \left(G;\hspace{0.33em}H) (resp. H H -substructure connectivity κ s ( G ; H ) {\kappa }^{s}\left(G;\hspace{0.33em}H) ) of G G is the cardinality of a minimum subgraph set such that every element of the set is isomorphic to H H (resp. every element of the set is isomorphic to a connected subgraph of H H ) in G G , whose vertices removal disconnects G G . In this article, we investigate the H H -structure connectivity and H H -substructure connectivity of the n n -dimensional burnt pancake network BP n {{\rm{BP}}}_{n} for each H ∈ { K 1 , K 1 , 1 , … , K 1 , n − 1 , P 4 , … , P 7 , C 8 } H\in \left\{{K}_{1},{K}_{1,1},\ldots ,{K}_{1,n-1},{P}_{4},\ldots ,{P}_{7},{C}_{8}\right\} .