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Spectral properties of a class of unicyclic graphs

The eigenvalues of G are denoted by [Formula: see text] , where n is the order of G. In particular, [Formula: see text] is called the spectral radius of G, [Formula: see text] is the least eigenvalue of G, and the spread of G is defined to be the difference between [Formula: see text] and [Formula:...

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Detalles Bibliográficos
Autor principal: Du, Zhibin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5415630/
https://www.ncbi.nlm.nih.gov/pubmed/28529433
http://dx.doi.org/10.1186/s13660-017-1367-2
Descripción
Sumario:The eigenvalues of G are denoted by [Formula: see text] , where n is the order of G. In particular, [Formula: see text] is called the spectral radius of G, [Formula: see text] is the least eigenvalue of G, and the spread of G is defined to be the difference between [Formula: see text] and [Formula: see text] . Let [Formula: see text] be the set of n-vertex unicyclic graphs, each of whose vertices on the unique cycle is of degree at least three. We characterize the graphs with the kth maximum spectral radius among graphs in [Formula: see text] for [Formula: see text] if [Formula: see text] , [Formula: see text] if [Formula: see text] , and [Formula: see text] if [Formula: see text] , and the graph with minimum least eigenvalue (maximum spread, respectively) among graphs in [Formula: see text] for [Formula: see text] .