### Abstract

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

Pages (from-to) | 19-30 |

Journal | Linear Algebra and its Applications |

Volume | 536 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

### Fingerprint

### Keywords

- Rose graphs
- Laplacian spectrum
- Closed walks
- Sachs' theorem
- Matchings

### Cite this

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*Linear Algebra and its Applications*, vol. 536, pp. 19-30. https://doi.org/10.1016/j.laa.2017.08.012

**Laplacian spectral characterization of roses.** / He, Changxiang; van Dam, Edwin.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Laplacian spectral characterization of roses

AU - He, Changxiang

AU - van Dam, Edwin

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A rose graph is a graph consisting of cycles that all meet in one vertex. We show that except for two specific examples, these rose graphs are determined by the Laplacian spectrum, thus proving a conjecture posed by Liu and Huang (2013) [8]. We also show that if two rose graphs have a so-called universal Laplacian matrix with the same spectrum, then they must be isomorphic. In memory of Horst Sachs (1927–2016), we show the specific case of the latter result for the adjacency matrix by using Sachs' theorem and a new result on the number of matchings in the disjoint union of paths.

AB - A rose graph is a graph consisting of cycles that all meet in one vertex. We show that except for two specific examples, these rose graphs are determined by the Laplacian spectrum, thus proving a conjecture posed by Liu and Huang (2013) [8]. We also show that if two rose graphs have a so-called universal Laplacian matrix with the same spectrum, then they must be isomorphic. In memory of Horst Sachs (1927–2016), we show the specific case of the latter result for the adjacency matrix by using Sachs' theorem and a new result on the number of matchings in the disjoint union of paths.

KW - Rose graphs

KW - Laplacian spectrum

KW - Closed walks

KW - Sachs' theorem

KW - Matchings

U2 - 10.1016/j.laa.2017.08.012

DO - 10.1016/j.laa.2017.08.012

M3 - Article

VL - 536

SP - 19

EP - 30

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -