On fat Hoffman graphs with smallest eigenvalue at least -3

Hye Jin Jang; Jack Koolen; Akihiro Munemasa; Tetsuji Taniguchi

doi:10.26493/1855-3974.262.a9d

On fat Hoffman graphs with smallest eigenvalue at least -3

Hye Jin Jang, Jack Koolen, Akihiro Munemasa, Tetsuji Taniguchi

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

We investigate fat Hoffman graphs with smallest eigenvalue at least -3, using their special graphs. We show that the special graph S(H) of an indecomposable fat Hoffman graph H is represented by the standard lattice or an irreducible root lattice. Moreover, we show that if the special graph admits an integral representation, that is, the lattice spanned by it is not an exceptional root lattice, then the special graph S-(H) is isomorphic to one of the Dynkin graphs A_n, D_n, or extended Dynkin graphs Ã_n or D̃_n.

Original language	English
Pages (from-to)	105-121
Number of pages	17
Journal	Ars Mathematica Contemporanea
Volume	7
Issue number	1
DOIs	https://doi.org/10.26493/1855-3974.262.a9d
Publication status	Published - 2014

Keywords

Graph eigenvalue
Hoffman graph
Line graph
Root system
Special graph

Access to Document

10.26493/1855-3974.262.a9d

Cite this

@article{4633d06528cc4ab68e85904176c5381b,

title = "On fat Hoffman graphs with smallest eigenvalue at least -3",

abstract = "We investigate fat Hoffman graphs with smallest eigenvalue at least -3, using their special graphs. We show that the special graph S(H) of an indecomposable fat Hoffman graph H is represented by the standard lattice or an irreducible root lattice. Moreover, we show that if the special graph admits an integral representation, that is, the lattice spanned by it is not an exceptional root lattice, then the special graph S-(H) is isomorphic to one of the Dynkin graphs An, Dn, or extended Dynkin graphs {\~A}n or {\~D}n.",

keywords = "Graph eigenvalue, Hoffman graph, Line graph, Root system, Special graph",

author = "Jang, {Hye Jin} and Jack Koolen and Akihiro Munemasa and Tetsuji Taniguchi",

year = "2014",

doi = "10.26493/1855-3974.262.a9d",

language = "English",

volume = "7",

pages = "105--121",

journal = "Ars Mathematica Contemporanea",

issn = "1855-3966",

publisher = "DMFA Slovenije",

number = "1",

}

TY - JOUR

T1 - On fat Hoffman graphs with smallest eigenvalue at least -3

AU - Jang, Hye Jin

AU - Koolen, Jack

AU - Munemasa, Akihiro

AU - Taniguchi, Tetsuji

PY - 2014

Y1 - 2014

N2 - We investigate fat Hoffman graphs with smallest eigenvalue at least -3, using their special graphs. We show that the special graph S(H) of an indecomposable fat Hoffman graph H is represented by the standard lattice or an irreducible root lattice. Moreover, we show that if the special graph admits an integral representation, that is, the lattice spanned by it is not an exceptional root lattice, then the special graph S-(H) is isomorphic to one of the Dynkin graphs An, Dn, or extended Dynkin graphs Ãn or D̃n.

AB - We investigate fat Hoffman graphs with smallest eigenvalue at least -3, using their special graphs. We show that the special graph S(H) of an indecomposable fat Hoffman graph H is represented by the standard lattice or an irreducible root lattice. Moreover, we show that if the special graph admits an integral representation, that is, the lattice spanned by it is not an exceptional root lattice, then the special graph S-(H) is isomorphic to one of the Dynkin graphs An, Dn, or extended Dynkin graphs Ãn or D̃n.

KW - Graph eigenvalue

KW - Hoffman graph

KW - Line graph

KW - Root system

KW - Special graph

UR - http://www.scopus.com/inward/record.url?scp=84892174074&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892174074&partnerID=8YFLogxK

U2 - 10.26493/1855-3974.262.a9d

DO - 10.26493/1855-3974.262.a9d

M3 - Article

AN - SCOPUS:84892174074

SN - 1855-3966

VL - 7

SP - 105

EP - 121

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

IS - 1

ER -

On fat Hoffman graphs with smallest eigenvalue at least -3

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this