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.CO2025
The Degree Polynomial
Jason I. Brown, Ian C. George
The degree polynomial of a multigraph is given by $\sum _{v \in V(G)} x^{\mbox{deg}(v)}$. We investigate here properties of the roots of such polynomials. In addition to examin…