Optimally reliable graphs for both edge and vertex failures
Trefor A Evans, Derek H. Smith · Networks · 1986
Abstract The problem of describing graphs representing a communication network which are optimally reliable has been studied both for the case of vertex failures and for the case of edge failures. We give a combinatorial definition in each case and show that under certain conditions the first definition implies the second. We use this result to investigate the existence of graphs which in some sense are optimally reliable with respect to both vertex and edge failures.