Reliability properties of the hypercube network (Q1102261)

It is well known that for a network with equal and independent edge failure probabilities \(\rho\), the most reliable networks are those with max \(\lambda\) and super \(\lambda\) properties, when \(\rho\) is small. In this paper we will show that the hypercube networks posses both max \(\lambda\) and super \(\lambda\) properties. In addition, some other properties such as point transitive, Hamiltonian and the average message distance of the hypercube network are also derived.