A graph with n nodes and e edges, where the nodes are perfectly reliable and the edges fail independently with equal probability p, is said to be uniformly optimally reliable (UOR) if it has the greatest reliability among all graphs with the same number of nodes and edges for all values of p. UOR simple graphs have been identified in the classes e = n − 1, e = n, e = n + 1, and e = n + 2. In this paper, we demonstrate that the UOR simple graphs in these classes are also UOR when the classes are extended to include multigraphs.
