A new method for constructing graphs determined by their generalized spectrum

A graph G is said to be determined by its generalized spectrum (DGS for short) if for any graph H, H and G are cospectral with cospectral complements implies that H is isomorphic to G  . Let Gˆ be the graph obtained from G by adding a pendent edge at every vertex of G  . We show that Gˆ is DGS if and only if G is DGS for some graph G  . This gives a simple way to construct large DGS graphs from small ones explicitly. In particular, we show that every graph in the infinite sequence G,Gˆ,Gˆˆ,⋯ is DGS, for some DGS graph G.