Edge-signed graphs with smallest eigenvalue greater than -2

Gary Greaves; Jack Koolen; Akihiro Munemasa; Yoshio Sano; Tetsuji Taniguchi

doi:10.1016/j.jctb.2014.07.006

Edge-signed graphs with smallest eigenvalue greater than -2

Gary Greaves, Jack Koolen, Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

情報科学研究科・情報基礎科学専攻

研究成果: Article › 査読

20 被引用数 (Scopus)

抄録

We give a structural classification of edge-signed graphs with smallest eigenvalue greater than -2. We prove a conjecture of Hoffman about the smallest eigenvalue of the line graph of a tree that was stated in the 1970s. Furthermore, we prove a more general result extending Hoffman's original statement to all edge-signed graphs with smallest eigenvalue greater than -2. Our results give a classification of the special graphs of fat Hoffman graphs with smallest eigenvalue greater than -3.

本文言語	English
ページ（範囲）	90-111
ページ数	22
ジャーナル	Journal of Combinatorial Theory. Series B
巻	110
DOI	https://doi.org/10.1016/j.jctb.2014.07.006
出版ステータス	Published - 2015 1月 1

ASJC Scopus subject areas

理論的コンピュータサイエンス
離散数学と組合せ数学
計算理論と計算数学

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10.1016/j.jctb.2014.07.006

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引用スタイル

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AU - Koolen, Jack

AU - Munemasa, Akihiro

AU - Sano, Yoshio

AU - Taniguchi, Tetsuji

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We give a structural classification of edge-signed graphs with smallest eigenvalue greater than -2. We prove a conjecture of Hoffman about the smallest eigenvalue of the line graph of a tree that was stated in the 1970s. Furthermore, we prove a more general result extending Hoffman's original statement to all edge-signed graphs with smallest eigenvalue greater than -2. Our results give a classification of the special graphs of fat Hoffman graphs with smallest eigenvalue greater than -3.

AB - We give a structural classification of edge-signed graphs with smallest eigenvalue greater than -2. We prove a conjecture of Hoffman about the smallest eigenvalue of the line graph of a tree that was stated in the 1970s. Furthermore, we prove a more general result extending Hoffman's original statement to all edge-signed graphs with smallest eigenvalue greater than -2. Our results give a classification of the special graphs of fat Hoffman graphs with smallest eigenvalue greater than -3.

KW - Hoffman conjecture

KW - Hoffman graphs

KW - Line graphs

KW - Signed graphs

KW - Smallest eigenvalue

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JO - Journal of Combinatorial Theory. Series B

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ER -

Edge-signed graphs with smallest eigenvalue greater than -2

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ASJC Scopus subject areas

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