Let  be a nontrivial connected graph. A set S of vertices of G is a semitotal dominating set if every vertex outside of S is adjacent to a vertex inside of S and every vertex inside of S is of distance at most 2 units from another vertex in S. A semitotal dominating set S of G is an isolate semitotal dominating set if the induced subgraph  contains at least one isolated vertex. The smallest cardinality  of an isolate semitotal dominating set is the isolate semitotal domination number of G.

This paper initiates the study of isolate semitotal domination in graphs. It determines the specific values of  for some special graphs and characterizes graphs G with small values of  Furthermore, this paper investigates the isolate semitotal dominating sets in the join and corona of graphs and, as a consequence, determines their corresponding isolate semitotal domination numbers.

isolate domination, semitotal domination, complete multipartite, join, corona