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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The spectrum of infinite regular line graphs


Author: Tomoyuki Shirai
Journal: Trans. Amer. Math. Soc. 352 (2000), 115-132
MSC (1991): Primary 39A12; Secondary 39A70
Published electronically: July 1, 1999
MathSciNet review: 1665338
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Abstract: Let $G$ be an infinite $d$-regular graph and $L(G)$ its line graph. We consider discrete Laplacians on $G$ and $L(G)$, and show the exact relation between the spectrum of $-\Delta _G$ and that of $-\Delta _{L(G)}$. Our method is also applicable to $(d_1,d_2)$-semiregular graphs, subdivision graphs and para-line graphs.


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Additional Information

Tomoyuki Shirai
Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan
Address at time of publication: Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
Email: shirai@neptune.ap.titech.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02497-6
PII: S 0002-9947(99)02497-6
Keywords: Regular line graph, subdivision, para-line graph, discrete Laplacian, spectrum
Received by editor(s): July 12, 1998
Published electronically: July 1, 1999
Article copyright: © Copyright 1999 American Mathematical Society