It is conjectured by Godsil Anna. Comb., 16 (2012), pp. 733--744 that the relative number of
controllable graphs compared to the total number of simple graphs on n vertices approaches …

In this paper, we consider the controllability problem for multi-agent networked control
systems. The main results of the paper are new graph-theoretic necessary conditions for …

In this article, we examine the controllability of Laplacian dynamic networks on cographs.
Cographs appear in modeling a wide range of networks and include as special instances …

Controllability is a fundamental issue concerning control of multi-agent networks and a very
important research topic in the modeling, analysis and coordination control of multi-agent …

The net Laplacian matrix of a signed graph G ̇ is defined to be NG ̇= DG ̇±− AG ̇,
where DG ̇±and AG ̇ are the diagonal matrix of net-degrees and the adjacency matrix of …

We study the eigenvectors and eigenvalues of random matrices with iid entries. Let N be a
random matrix with iid entries which have symmetric distribution. For each unit eigenvector v …

In this letter, the directed threshold graphs (DTGs) and their Laplacian controllability issues
are studied. The graphs are constructed by a sequence of graph operations that include …

If G is a graph with n vertices, AG is its adjacency matrix and b is a binary vector of length n,
then the pair (AG, b) is said to be controllable (or G is said to be controllable for the vector b) …

In this paper, we investigate the controllability of a linear time-invariant network following a
Laplacian dynamics defined on a threshold graph. In this direction, by considering the modal …

This paper is concerned with the problem of constructing a controllable graph subject to
some practical edge constraints. Specifically, suppose the total amount of vertices and the …