Maximal-status conjecture for radial Moore graphs

Let $G_d$ be the radial Moore graph of degree $d$, and let the status of a vertex be the sum of its distances to all vertices of $G_d$. Maximal-status conjecture. The radial Moore graph $G_d$ has maximal status for all $d \geq 3$. The paper establishes upper bounds on the status of radial Moore graphs of diameter $3$ and presents an infinite family with high status; the asserted maximality is proposed as an open problem.