Controllable graphs

D. Cvetković, P. Rowlinson, Z. Stanić, M. G. Yoon

The eigenvalues of a graph are the eigenvalues of its adjacency matrix. An eigenvalue of a graph is called {\em main} if the corresponding eigenspace contains a vector for which the sum of coordinates is different from 0. Connected graphs in which all eigenvalues are mutually distinct and main have recently attracted attention in control theory.