Laplacian spectral characterization of some graph products

This paper studies the Laplacian spectral characterization of some graph products. We consider a class of connected graphs: , and characterize all graphs G∈G such that the products G×Km are L-DS graphs. The main result of this paper states that, if G∈G, except for C6, is a L-DS graph, so is the product G×Km. In addition, the L-cospectral graphs with C6×Km have been found.