5 problems

Let $d_1,d_2\in\mathbb{Z}^+$ and let $m$ satisfy the Grimm–Ballew procedure's conditions; let $g_1$ and $g_2$ be different bases obtained by that procedure for the same $d_1$,…

Complete Young graph conjecture. A Young graph is a complete graph if and only if it has at least one nonzero diagonal-labelled node $[r,r]$.

Complete graph counting conjecture. The $(g,k)$ Young graph is the complete graph $K_m$ if and only if there are exactly $m-1$ distinct integers $r$ for which $a<g$ and both $a$ an…

1089 graph endpoint conjecture. If there is a $(g,k)$-reverse multiple with $a_0+a_{n-1}=g$, then the Young graph is the 1089 graph. Conversely, if the graph is the 1089 graph, the…

1089 graph conjecture. The $(g,k)$ Young graph is isomorphic to the 1089 graph if and only if $k+1$ divides $g$.