Non-realizability conjecture for complete bipartite strong resolving graphs

Let $G$ be a connected graph, and let $G_{SR}$ denote its strong resolving graph, whose vertices are the mutually maximally distant vertices of $G$, with adjacency between distinct mutually maximally distant vertices. For integers $r,s\ge 2$, consider the graph equation

$$G_{SR}\cong K_{r,s}.$$

Complete bipartite strong resolving graph conjecture. The graph equation $G_{SR}\cong K_{r,s}$ has no solution for any $r,s\ge 2$.

This conjecture extends the known non-realizability of the equations $G_{SR}\cong K_{1,r}$ and $G_{SR}\cong K_{2,r}$ for $r\ge 2$. It asks whether no complete bipartite graph with both parts of size at least two can occur as a strong resolving graph.