Unbalanced unicyclic and bicyclic graphs with extremal spectral radius

Francesco Belardo; Maurizio Brunetti; Adriana Ciampella

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 2, page 417-433
  • ISSN: 0011-4642

Abstract

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A signed graph Γ is a graph whose edges are labeled by signs. If Γ has n vertices, its spectral radius is the number ρ ( Γ ) : = max { | λ i ( Γ ) | : 1 ≤ i ≤ n } , where λ 1 ( Γ ) ≥ ⋯ ≥ λ n ( Γ ) are the eigenvalues of the signed adjacency matrix A ( Γ ) . Here we determine the signed graphs achieving the minimal or the maximal spectral radius in the classes 𝔘 n and 𝔅 n of unbalanced unicyclic graphs and unbalanced bicyclic graphs, respectively.

How to cite

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Belardo, Francesco, Brunetti, Maurizio, and Ciampella, Adriana. "Unbalanced unicyclic and bicyclic graphs with extremal spectral radius." Czechoslovak Mathematical Journal 71.2 (2021): 417-433. <http://eudml.org/doc/297792>.

@article{Belardo2021,
abstract = {A signed graph $\Gamma $ is a graph whose edges are labeled by signs. If $\Gamma $ has $n$ vertices, its spectral radius is the number $\rho (\Gamma ) := \max \lbrace | \lambda _i(\Gamma ) | \colon 1 \le i \le n \rbrace $, where $\lambda _1(\Gamma ) \ge \cdots \ge \lambda _n(\Gamma )$ are the eigenvalues of the signed adjacency matrix $A(\Gamma )$. Here we determine the signed graphs achieving the minimal or the maximal spectral radius in the classes $\mathfrak \{U\}_n$ and $\mathfrak \{B\}_n$ of unbalanced unicyclic graphs and unbalanced bicyclic graphs, respectively.},
author = {Belardo, Francesco, Brunetti, Maurizio, Ciampella, Adriana},
journal = {Czechoslovak Mathematical Journal},
keywords = {signed graph; spectral radius; bicyclic graph},
language = {eng},
number = {2},
pages = {417-433},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Unbalanced unicyclic and bicyclic graphs with extremal spectral radius},
url = {http://eudml.org/doc/297792},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Belardo, Francesco
AU - Brunetti, Maurizio
AU - Ciampella, Adriana
TI - Unbalanced unicyclic and bicyclic graphs with extremal spectral radius
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 2
SP - 417
EP - 433
AB - A signed graph $\Gamma $ is a graph whose edges are labeled by signs. If $\Gamma $ has $n$ vertices, its spectral radius is the number $\rho (\Gamma ) := \max \lbrace | \lambda _i(\Gamma ) | \colon 1 \le i \le n \rbrace $, where $\lambda _1(\Gamma ) \ge \cdots \ge \lambda _n(\Gamma )$ are the eigenvalues of the signed adjacency matrix $A(\Gamma )$. Here we determine the signed graphs achieving the minimal or the maximal spectral radius in the classes $\mathfrak {U}_n$ and $\mathfrak {B}_n$ of unbalanced unicyclic graphs and unbalanced bicyclic graphs, respectively.
LA - eng
KW - signed graph; spectral radius; bicyclic graph
UR - http://eudml.org/doc/297792
ER -

References

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