# Domination problem is NPC

I call the problem as DOM. Given a graph $$G$$ and an integer $$d$$, Decision problem DOM - "Does there exists a dominating set of size less than or equal to 'd' in G? " DOM is NP Complete problem. But, if we specify some class of graphs $$G'$$ and if we ask the same question, then DOM might be solved in polynomial time. (Eg : Given $$C_n$$, and an integer $$d$$ , you can verify DOM in polynomial time ) Till date , for which all classes of graphs, DOM problem can be solved in polynomial time ? [Let me know where I can find research papers worked on this topic]