  A neighborhood star-free graph is one in which every vertex of degree at
least two is contained in a triangle. This class has been considered before, in
the context of edge domination. In the present paper, we study the complexity
of the dominating induced matching problem for the class, and prove that the
corresponding decision problem is NP-complete for several subclasses of
neighborhood star-free graphs. In addition, we show that the dominating induced
matching problem can be solved in polynomial time for neighborhood star-free
graphs, containing no crickets as induced subgraphs.

Discrete Mathematics;Combinatorics