6 problems

Defect-2 nonexistence conjecture. There are no $(\Delta,D,-2)$-graphs with $\Delta\ge 4$ and $D\ge 4$.

Let $d,k\geq 2$. A $(d,k;+1)$-digraph is a $k$-geodetic digraph with minimum out-degree $d$ and order … where … is the directed Moore bound. Nonexistence conjecture. There are no…

Total-regularity conjecture. Any mixed graph with excess one is totally regular.

Total regularity conjecture. All $(r,z,k;-1)$- and $(r,z,k;+1)$-graphs are totally regular.

A graph with defect or excess $2$ is said to have cyclic defect or excess when its defect or excess matrix is the adjacency matrix of a cycle. The Möbius ladder on $8$ vertices is…

The Moore bound is an upper bound for the order of a graph with maximum degree $d$ and diameter $D$, and a lower bound for the order of a graph with minimum degree $d$ and odd girt…