The competition numbers of ternary Hamming graphs

It is known to be a hard problem to compute the competition number k(G) of a graph G in general. Park and Sano [13] gave the exact values of the competition numbers of Hamming graphs H(n,q) if $1\le n\le 3$ or $1\le q\le 2$. In this paper, we give an explicit formula of the competition numbers of ternary Hamming graphs.