The competition numbers of ternary Hamming graphs

It is known to be a hard problem to compute the competition number k(G)k(G) of a graph GG in general. Park and Sano (in press) [16] gave the exact values of the competition numbers of Hamming graphs H(n,q)H(n,q) if 1≤n≤31≤n≤3 or 1≤q≤21≤q≤2. In this paper, we give an explicit formula for the competition numbers of ternary Hamming graphs.