The spectrum of infinite regular line graphs

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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 -Δc and that of -ΔL(G), Our method is also applicable to (d1,d2)-seiniregular graphs, subdivision graphs and para-line graphs.

Original languageEnglish
Pages (from-to)115-132
Number of pages18
JournalTransactions of the American Mathematical Society
Issue number1
Publication statusPublished - 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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