Bounds of Two-Terminal Network Reliability and Base Spectrum of Network Graph

The base spectrum is a set of effectively computable graph parameters. Its components are the frameness and the forestness of the graph.
The significance of the base spectrum for derivation of effective bounds on the all- and two-terminal network reliability is demonstrated. Several related conjectures are formulated. For certain classes of graphs, upper bounds for two-terminal reliability are derived; these bounds confirm one of the above conjectures.