### 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 -Δc and that of -Δ_{L(G)}, Our method is also applicable to (d_{1},d_{2})-seiniregular graphs, subdivision graphs and para-line graphs.

Original language | English |
---|---|

Pages (from-to) | 115-132 |

Number of pages | 18 |

Journal | Transactions of the American Mathematical Society |

Volume | 352 |

Issue number | 1 |

Publication status | Published - Dec 1 2000 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*352*(1), 115-132.

**The spectrum of infinite regular line graphs.** / Shirai, Tomoyuki.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 352, no. 1, pp. 115-132.

}

TY - JOUR

T1 - The spectrum of infinite regular line graphs

AU - Shirai, Tomoyuki

PY - 2000/12/1

Y1 - 2000/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=22844454199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22844454199&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:22844454199

VL - 352

SP - 115

EP - 132

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -