The inverse eigenvalue problem of a given graph G is to determine all possible spectra of
real symmetric matrices whose off-diagonal entries are governed by the adjacencies in G …

For an n× n matrix A, let q (A) be the number of distinct eigenvalues of A. If G is a connected
graph on n vertices, let S (G) be the set of all real symmetric n× n matrices A=[aij] such that …

AL Cauchy proved that if the vertex-edge graphs of two convex polyhedra are isomorphic
and corresponding faces are congruent then the two polyhedra are the same. This result …

Abstract We propose a Nordhaus–Gaddum conjecture for q (G), the minimum number of
distinct eigenvalues of a symmetric matrix corresponding to a graph G: for every graph G …

We establish new bounds on the minimum number of distinct eigenvalues among real
symmetric matrices with nonzero off-diagonal pattern described by the edges of a graph and …

For a graph $ G $, we associate a family of real symmetric matrices, $\mathcal {S}(G) $,
where for any $ M\in\mathcal {S}(G) $, the location of the nonzero off-diagonal entries of $ M …

The inverse eigenvalue problem of a graph studies the real symmetric matrices whose off-
diagonal pattern is prescribed by the adjacencies of the graph. The strong spectral property …

The parameter q (G) of a graph G is the minimum number of distinct eigenvalues over the
family of symmetric matrices described by G. It is shown that the minimum number of edges …

We introduce a notion of compatibility for multiplicity matrices. This gives rise to a necessary
condition for the join of two (possibly disconnected) graphs G and H to be the pattern of an …

The parameter $ q (G) $ of an $ n $-vertex graph $ G $ is the minimum number of distinct
eigenvalues over the family of symmetric matrices described by $ G $. We show that all $ G …