## Abstract

The product graph *G _{m} *G_{p}* of two given graphs

*G*and

_{m}*G*, defined by J.C. Bermond et al.[J Combin Theory, Series B 36(1984) 32-48] in the context of the so-called (

_{p}*Δ,D*)-problem, is one interesting model in the design of large reliable networks. This work deals with sufficient conditions that guarantee these product graphs to be hamiltonian-connected. Moreover, we state product graphs for which provide panconnectivity of interconnection networks modeled by a product of graphs with faulty elements.