The spectrum of infinite regular line graphs

Shirai, Tomoyuki

doi:10.1090/S0002-9947-99-02497-6

The spectrum of infinite regular line graphs
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by Tomoyuki Shirai PDF

Trans. Amer. Math. Soc. 352 (2000), 115-132 Request permission

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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