In this work, we consider the optimization problem of maximizing the number of spanning trees among graphs and multigraphs in the same class, i.e. having a fixed number of nodes and a fixed number of edges. Since a spanning tree is a minimally connected subgraph, graphs and multigraphs having more of these are, in some sense, immune to disconnection by edge failure. The authors envision this as a research aid that is of particular interest to graduate students or advanced undergraduate students and researchers in the area of network reliability theory. This would encompass graph theorists of...