Written for mathematicians working with the theory of graph spectra, this book explores more
than 400 inequalities for eigenvalues of the six matrices associated with finite simple graphs …

In this paper, we consider the problem of obtaining graph-theoretic characterizations of
controllability for the Laplacian-based leader-follower dynamics. Our developments rely on …

An eigenvalue λ of a graph G of order n is a main eigenvalue if its eigenspace is not
orthogonal to the all-ones vector j. In 1978, Cvetković proved that G has exactly one main …

A distance based on the exponential kernel of the adjacency matrix of a graph and
representing how well two vertices connect to each other in a graph is defined and studied …

An eigenvalue λ of a graph G of order n is a main eigenvalue if its eigenspace is not
orthogonal to the all-ones vector j n. In 1978, Cvetković proved that G has exactly one main …

We give a survey of graph spectral techniques used in computer sciences. The survey
consists of a description of particular topics from the theory of graph spectra independently …

An eigenvalue μ of a graph G of order n is a main eigenvalue if its eigenspace is not
orthogonal to the all-ones vector e. Characterizing graphs with s (2≤ s≤ n) number of main …

Connected graphs whose eigenvalues are distinct and main are called controllable graphs
in view of certain applications in control theory. We give some general characterizations of …

In control theory, networked dynamical systems have a wide range of engineering
applications. In a relational graph among followers (F) and leaders (R), new necessary and …

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 …