Displaying similar documents to “On the inverse eigenvalue problem for a special kind of acyclic matrices”

Extremal inverse eigenvalue problem for matrices described by a connected unicyclic graph

Bijoya Bardhan, Mausumi Sen, Debashish Sharma (2024)

Applications of Mathematics

Similarity:

In this paper, we deal with the construction of symmetric matrix whose corresponding graph is connected and unicyclic using some pre-assigned spectral data. Spectral data for the problem consist of the smallest and the largest eigenvalues of each leading principal submatrices. Inverse eigenvalue problem (IEP) with this set of spectral data is generally known as the extremal IEP. We use a standard scheme of labeling the vertices of the graph, which helps in getting a simple relation between...

Eigenvalue Conditions for Induced Subgraphs

Jochen Harant, Julia Niebling, Sebastian Richter (2015)

Discussiones Mathematicae Graph Theory

Similarity:

Necessary conditions for an undirected graph G to contain a graph H as induced subgraph involving the smallest ordinary or the largest normalized Laplacian eigenvalue of G are presented.

A note on certain ergodicity coeflcients

Francesco Tudisco (2015)

Special Matrices

Similarity:

We investigate two ergodicity coefficients ɸ ∥∥ and τn−1, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized version have been shown so far.We provide a further result concerning the limit of its powers. Then we propose a generalization of the second coefficient τ n−1 and we show that, under mild conditions, it can be used to recast the eigenvector...

A generalization of the graph Laplacian with application to a distributed consensus algorithm

Guisheng Zhai (2015)

International Journal of Applied Mathematics and Computer Science

Similarity:

In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of a graph Laplacian by extending the adjacency weights (or weighted interconnection coefficients) from scalars to matrices. More precisely, we use positive definite matrices to denote full multi-dimensional interconnections, while using nonnegative definite matrices to denote partial multi-dimensional interconnections. We prove that the generalized graph Laplacian inherits the...

Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string

Behrouz Emamizadeh, Amin Farjudian (2014)

Nonautonomous Dynamical Systems

Similarity:

In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the difference between the densities of the two materials is sufficiently small. Finally, a simple numerical algorithm will be presented which will...