  A sequence $S=(v_1,\ldots,v_k)$ of distinct vertices of a graph $G$ is called
a legal sequence if $N[v_i] \setminus \cup_{j=1}^{i-1}N[v_j]\not=\emptyset$ for
any $i$. The maximum length of a legal (dominating) sequence in $G$ is called
the Grundy domination number $\gamma_{gr}(G)$ of a graph $G$. It is known that
the problem of determining the Grundy domination number is NP-complete in
general, while efficient algorithm exist for trees and some other classes of
graphs. In this paper we find an efficient algorithm for the Grundy domination
number of an interval graph. We also show the exact value of the Grundy
domination number of an arbitrary Sierpi\'{n}ski graph $S_p^n$, and present
algorithms to construct the corresponding sequence. These results are obtained
by using the main result of the paper, which are sharp bounds for the Grundy
domination number of a vertex- and edge-removed graph. That is, given a graph
$G$, $e\in E(G)$, and $u\in V(G)$, we prove that $\gamma_{gr}(G)-1\le
\gamma_{gr}(G-e) \le \gamma_{gr}(G)+1$ and $\gamma_{gr}(G)-2\le
\gamma_{gr}(G-u) \le \gamma_{gr}(G)$. For each of the bounds there exist
graphs, in which all three possibilities occur for different edges,
respectively vertices.
