The domination number and the least Q-eigenvalue

In this paper, for a nonbipartite graph with both order n and domination number γ, we show that it contains a nonbipartite unicyclic spanning subgraph with the same domination number γ. We also present some results about the changing of the domination number when the structure of a graph is changed. By investigating the relation between the domination number and the least Q-eigenvalue of a graph, we minimize the least Q  -eigenvalue among all the nonbipartite graphs with both order n⩾4n⩾4 and given domination number γ⩽n+13.