On double bound graphs with respect to graph operations

We consider upper bound graphs with respect to operations on graphs, for example, the sum, the Cartesian product, the corona and the middle graphs of graphs, etc. According to the characterization of double bound graphs, we deal with characterizations of double bound graphs obtained by graph operations. For example, The Cartesian product G x H of two graphs G and H is a DB-graph if and only if both G and H are bipartite graphs, the corona G circle H of two graphs G and H is a DB-graph if and only if G is a bipartite graph and H is a UB-graph, and the middle graph M(G) of a graph G is a DB-graph if and only if G is an even cycle or a path, etc.