Fault Tolerance of Novel Compound Graph Based on Disc-Ring and Folded Hypercube

Multiprocessor systems commonly take interconnection network (simply graph) as the underlying topological structure. The performance of multiprocessor systems is greatly influenced by its interconnection topology. The connectivity is a classical metric to evaluate the fault tolerance of multiprocessor systems. In this work, we propose a new class of compound graph based on disc-ring and folded hypercube, $DFQ(m,d,n)$ ($DFQ_n$), to improve the diameter of the newly proposed compound graph DQcube ($DQ_n$). In this paper, we first show that the connectivity, edge-connectivity and tightly super connectivity are $n+2$, $n+2$ and $n+2$, respectively. Furthermore, we show that $h$-extra connectivity of $DFQ_n$ is $\kappa_h(DFQ_n)=(h+1)(n+2)-2h-\tbinom{h}{2}$