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Leading eigenvalues of adjacency matrices of star-like graphs with fixed numbers of vertices and edges

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abstract
For a sequence of adjacency matrices, describing the unfolding of a network from the graph of a star, through graphs of a broom, to the graph of a link with constant vertices and edges, we show that the leading eigenvalue (the spectral radius) satisfies a simple algebraic equation. The equation allows easy numerical computation of the leading eigenvalue as well as a direct proof of its monotonicity in terms of the maximal degree of vertices.
subject
Leading eigenvalue
Adjacency matrix
infectious disease model
contributor
Fries, W. (author)
Jiang, M. (author)
date
2020-03-23T17:48:37Z (accessioned)
2020-03-23T17:48:37Z (available)
6/8/19 (issued)
identifier
Fries, W. D., & Jiang, M. (2019). Leading eigenvalues of adjacency matrices of star-like graphs with fixed numbers of vertices and edges. Cogent Mathematics & Statistics, (just-accepted), 1628513. (citation)
https://doi.org/10.1080/25742558.2019.1628513 (doi)
http://hdl.handle.net/10339/96605 (uri)
language
en (iso)
publisher
Cogent
rights
https://creativecommons.org/licenses/by/4.0/ (uri)
source
Applied & Interdisciplinary Mathematic
title
Leading eigenvalues of adjacency matrices of star-like graphs with fixed numbers of vertices and edges
type
Article

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