Leading eigenvalues of adjacency matrices of star-like graphs with fixed numbers of vertices and edges
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Leading eigenvalues of adjacency matrices of star-like graphs with fixed numbers of vertices and edges, William D. Fries & Miaohua Jiang, Cogent Mathematics & Statistics (2019), 6: 1628513.Journal
COGENT MATHEMATICS & STATISTICSRights
Copyright © 2019 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.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.Note
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2574-2558Version
Final published versionae974a485f413a2113503eed53cd6c53
10.1080/25742558.2019.1628513
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Except where otherwise noted, this item's license is described as Copyright © 2019 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license.