The b-chromatic number of the tensor product of distinct star graphs

Let $G$ be the tensor product of two distinct star graphs $S_n$ and $S_m$. Star-graph tensor-product conjecture. The $b$-chromatic number of $G$ is $m+n+1$. This conjecture proposes a general formula for the $b$-chromatic number of tensor products of distinct star graphs; the supplied text gives no evidence that it has been resolved.