Acta Mathematica Hungarica
Volume/Issue:
Volume 114: Issue 1-2
On the multiplicity of the eigenvalues of a graph
Authors:
José de la Pena UNAM. Cd. Universitaria Instituto de Matemáticas México 04510 D.F.

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and
Juan Rada Universidad de los Andes Departamento de Matemáticas, Facultad de Ciencias Mérida Venezuela

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Pages:
91–101
Online Publication Date:
22 Nov 2006
Publication Date:
01 Jan 2007
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-006-0515-9
Keywords:
Hermitian matrix; eigenvalues; characteristic polynomial; energy of a graph; 05C50; 15A48
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Abstract  

Given a graph G with characteristic polynomial ϕ(t), we consider the ML-decomposition ϕ(t) = q1(t)q2(t)2 ... qm(t)m, where each qi(t) is an integral polynomial and the roots of ϕ(t) with multiplicity j are exactly the roots of qj(t). We give an algorithm to construct the polynomials qi(t) and describe some relations of their coefficients with other combinatorial invariants of G. In particular, we get new bounds for the energy E(G) =
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathop \sum \limits_{i = 1}^n$$ \end{document}
|λi| of G, where λ1, λ2, ..., λn are the eigenvalues of G (with multiplicity). Most of the results are proved for the more general situation of a Hermitian matrix whose characteristic polynomial has integral coefficients.
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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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