  In the paper, we write a linear algorithm for calculating the weighted
domination number of a vertex-weighted cactus. The algorithm is based on the
well known depth first search (DFS) structure. Our algorithm needs less than
$12n+5b$ additions and $9n+2b$ $\min$-operations where $n$ is the number of
vertices and $b$ is the number of blocks in the cactus.
