  In a graph $G=(V,E)$ with no isolated vertex, a dominating set $D \subseteq
V$, is called a semitotal dominating set if for every vertex $u \in D$ there is
another vertex $v \in D$, such that distance between $u$ and $v$ is at most two
in $G$. Given a graph $G=(V,E)$ without isolated vertices, the Minimum
Semitotal Domination problem is to find a minimum cardinality semitotal
dominating set of $G$. The semitotal domination number, denoted by
$\gamma_{t2}(G)$, is the minimum cardinality of a semitotal dominating set of
$G$. The decision version of the problem remains NP-complete even when
restricted to chordal graphs, chordal bipartite graphs, and planar graphs.
Galby et al. in [6] proved that the problem can be solved in polynomial time
for bounded MIM-width graphs which includes many well known graph classes, but
left the complexity of the problem in strongly chordal graphs unresolved.
Henning and Pandey in [20] also asked to resolve the complexity status of the
problem in strongly chordal graphs. In this paper, we resolve the complexity of
the problem in strongly chordal graphs by designing a linear-time algorithm for
the problem.
