MSGSS
On the Real Reliability Roots of Graphs
There are many ways to model a network’s robustness to random failure. In one such method, consider a connected graph $G$, and assume that every edge fails independently with probability $q$. The {\em (all-terminal) reliability polynomial} (or just {\em Reliability Polynomial}) is the probability in $q$ that the spanning connected subgraph of operational edges is connected. In this presentation we will explore two recent results involving the real roots of reliability polynomials of simple graphs.