6 problems

Boesch's conjecture. Each uniformly most reliable graph in $\mathcal{C}_{n,m}$ is a $0$-element in $\mathcal{C}_{n,m}$.

Let $d$ be a prescribed average degree, and consider graphs with average degree $d$. Reliability is measured by the average of the reliability polynomial, which quantifies robustne…

Let $FCG_{n,c}$ denote the fair cake-cutting graph with parameters $n$ and $c$. A graph is uniformly most reliable for fixed order $n$ and size $m$ if its reliability polynomial is…

N-1 redundancy sparsity conjecture. This sparsity is a natural property of the N-1 redundancy engineered into electrical networks.

Mesh-network bondage conjecture. For $m\geqslant 5$,

Edge-connectivity UBB conjecture. If