  For integers r and k > 0(k>r),a conditional (k, r)-coloring of a graph G is a
proper k-coloring of G such that every vertex v of G has at least min{r,d(v)}
differently colored neighbors, where d(v) is the degree of v. In this note, for
different values of r we obtain the conditional chromatic number of a grid
$G(2,n) \cong P_2 \ \Box \ P_n$, $C_n^2$ and the strong product of $P_n$ and
$P_m$ (n,m being positive integers). Also, for integers $n \geq 3$ and $t \geq
1$ the second order conditional chromatic number (also known as dynamic
chromatic number) of the (t,n)-web graph is obtained.
