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 (in press) [16] gave the exact values of the competition numbers of Hamming graphs H ( n , q ) if 1 ≤ n ≤ 3 or 1 ≤ q ≤ 2 . In this paper, we give an explicit formula for the competition numbers of ternary Hamming graphs.