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Let $F$ be an algebraically closed field of prime characteristic $p$. Themodular McKay graph of $G:=SL_n(p)$ with respect to its standard $FG$-module$W$ is the connected, directed graph whose vertices are the irreducible$FG$-modules and for which there is an edge from a vertex $V_1$ to $V_2$ if$V_2$ occurs as a composition factor of the tensor product $V_1 \otimes W$. Weshow that the diameter of this modular McKay graph is $\frac{1}{2}(p-1)(n^2-n)$.

On the modular McKay graph of $SL_n(p)$ with respect to its standard representation