Controllability of NEPSes of graphs

If G is a graph with n vertices, A G is its adjacency matrix and b is a binary vector of length n, then the pair (A G, b) is said to be controllable (or G is said to be controllable for the vector b) if A G has no eigenvector orthogonal to b. In particular, if b is the all-1 vector j, then we simply say that G is controllable. In this paper, we consider the controllability of non-complete extended p-sums (for short, NEPSes) of graphs. We establish some general results and then focus the attention to the controllability of paths and related NEPSes. Moreover, the controllability of Cartesian products and tensor products is also considered. Certain related results concerning signless Laplacian matrices and signed graphs are reported.