Can one reduce the size of a graph without significantly altering its basic properties? The
graph reduction problem is hereby approached from the perspective of restricted spectral …

In order to become worldly things, that is, deeds and facts and events and patterns of
thoughts or ideas,[action, speech, and thought] must first be seen, heard, and remembered …

How does coarsening affect the spectrum of a general graph? We provide conditions such
that the principal eigenvalues and eigenspaces of a coarsened and original graph …

Graph filters play a key role in processing the graph spectra of signals supported on the
vertices of a graph. However, despite their widespread use, graph filters have been …

We present a characterization of eigenvalue inequalities between two Hermitian matrices by
means of inertia indices. As applications, we deal with some classical eigenvalue …

Given a connected regular graph G, let l (G) be its line graph, s (G) its subdivision graph, r
(G) the graph obtained from G by adding a new vertex corresponding to each edge of G and …

Given a graph we can associate several matrices which record information about vertices
and how they are interconnected. The question then arises, given that you know the …

Let L n be a linear hexagonal chain with n hexagons. In this paper, according to the
decomposition theorem of normalized Laplacian polynomial of a graph, we obtain that the …

Determining and analyzing the spectra of graphs is an important and exciting research topic
in mathematics science and theoretical computer science. The eigenvalues of the …

The eigenvalues of the normalized Laplacian matrix of a network play an important role in its
structural and dynamical aspects associated with the network. In this paper, we study the …