Let G = (V, E) be a graph and k be a positive integer. A

-dominating set of G is a subset

such that each vertex in

has at least

neighbors in S. A Roman

-dominating function on G is a function

: V

{0, 1, 2} such that every vertex

with

= 0 is adjacent to at least

vertices

,

,

,

with

= 2 for

= 1, 2,

,

. In the paper titled "Roman

-domination in graphs" (J. Korean Math. Soc. 46 (2009), no. 6, 1309-1318) K. Kammerling and L. Volkmann showed that for any graph G with

vertices,

min

, and the equality holds if and only if

or

and

or

and G or

has a vertex of degree

- 1 and its complement has a vertex of degree

- 2. In this paper we find a counterexample of Kammerling and Volkmann's result and then give a correction to the result.