Leading eigenvalues of adjacency matrices of star-like graphs with fixed numbers of vertices and edges
AffiliationUniv Arizona, Dept Math
MetadataShow full item record
PublisherTAYLOR & FRANCIS AS
CitationLeading 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.
JournalCOGENT MATHEMATICS & STATISTICS
RightsCopyright © 2019 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license.
Collection InformationThis 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 email@example.com.
AbstractFor 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.
NoteOpen access journal
VersionFinal published version