Local Optimality of Mixed Reliability for Several Classes of Networks with Fixed Sizes

Abstract

In this work, the local optimality of mixed reliability of networks is surveyed. A reliability comparison criterion related with subgraphs to measure the local optimality of the mixed reliability of networks is established. Using the comparison criterion, we characterize all locally optimally mixed reliable networks among all n-vertex networks with fixed sizes m=n, m=n+1 and m=n+2, respectively.