D-Spectra for Networks with Binary and Ternary Components

Network reliability is an important problem from both theoretical and practical points of view. One of the most powerful approaches for handling this problem is by using a so-called D-spectra method. We describe the D-spectra for two-state networks with binary and ternary components and give an overview of its principal combinatorial properties. In particular, we establish an important connection between the D-spectra and the number of network's failure sets of a given size.