Weighted graphs: Eigenvalues and chromatic number

<p>We revisit Hoffman relation involving chromatic number $\chi$ and eigenvalues. We construct some graphs and weighted graphs such that the largest and smallest eigenvalues $\lambda$ dan $\mu$ satisfy $\lambda=(1-\chi)\mu.$ We study in particular the eigenvalues of the integer simplex $T_m^2,...

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Bibliographic Details
Main Author:	Charles Delorme
Format:	Article
Language:	English
Published:	Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 2016-04-01
Series:	Electronic Journal of Graph Theory and Applications
Subjects:	graph spectra chromatic number
Online Access:	https://www.ejgta.org/index.php/ejgta/article/view/62

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spelling	doaj-93c8e0a88fe94ac1b621ea2e9cf217c32021-03-11T01:13:04ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872016-04-014181710.5614/ejgta.2016.4.1.253Weighted graphs: Eigenvalues and chromatic numberCharles Delorme0University Paris Sud 91405 Orsay CEDEX - France<p>We revisit Hoffman relation involving chromatic number $\chi$ and eigenvalues. We construct some graphs and weighted graphs such that the largest and smallest eigenvalues $\lambda$ dan $\mu$ satisfy $\lambda=(1-\chi)\mu.$ We study in particular the eigenvalues of the integer simplex $T_m^2,$ a 3-chromatic graph on $\binom {m+2}{2}$ vertices.</p>https://www.ejgta.org/index.php/ejgta/article/view/62graph spectrachromatic number
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Charles Delorme
spellingShingle	Charles Delorme Weighted graphs: Eigenvalues and chromatic number Electronic Journal of Graph Theory and Applications graph spectra chromatic number
author_facet	Charles Delorme
author_sort	Charles Delorme
title	Weighted graphs: Eigenvalues and chromatic number
title_short	Weighted graphs: Eigenvalues and chromatic number
title_full	Weighted graphs: Eigenvalues and chromatic number
title_fullStr	Weighted graphs: Eigenvalues and chromatic number
title_full_unstemmed	Weighted graphs: Eigenvalues and chromatic number
title_sort	weighted graphs: eigenvalues and chromatic number
publisher	Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
series	Electronic Journal of Graph Theory and Applications
issn	2338-2287
publishDate	2016-04-01
description	<p>We revisit Hoffman relation involving chromatic number $\chi$ and eigenvalues. We construct some graphs and weighted graphs such that the largest and smallest eigenvalues $\lambda$ dan $\mu$ satisfy $\lambda=(1-\chi)\mu.$ We study in particular the eigenvalues of the integer simplex $T_m^2,$ a 3-chromatic graph on $\binom {m+2}{2}$ vertices.</p>
topic	graph spectra chromatic number
url	https://www.ejgta.org/index.php/ejgta/article/view/62
work_keys_str_mv	AT charlesdelorme weightedgraphseigenvaluesandchromaticnumber
_version_	1714790892053725184

Weighted graphs: Eigenvalues and chromatic number

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