L(2,1)-labeling of a circular graph

In this paper the A-number of the circular graph C(km,m) is shown at most 9 where m >= 3 and k >= 2, and the lambda-number of the circular graph C(km+s, m) is shown at most 15 where m >= 3, k >= 2 and 1 <= s <= m - 1. In particular, the lambda-numbers of C(2m, m) and C(n, 2) are determined, which are at most 8. All our results indicates that the Griggs and Yeh's conjecture holds for circular graphs. The conjecture says that for any graph G with maximum degree Delta >= 2, lambda(G) <= Delta(2). Also, we determine A-numbers of C(n, 3), C(n, 4) and C(n, 5) if n equivalent to 0(mod 7).