2 papers
math.CO2026
On the Real Reliability Roots of Graphs
Jason I. Brown, Isaac McMullin
Consider a connected graph , and assume that every edge fails independently with probability . The {\em (all-terminal) reliability polynomial} is the probability in that…
math.CO2023
On the Split Reliability of Graphs
Jason I. Brown, Isaac McMullin
A common model of robustness of a graph against random failures has all vertices operational, but the edges independently operational with probability . One can ask for the prob…