### Abstract

Original language | English |
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Journal | Discrete Applied Mathematics |

DOIs | |

Publication status | E-pub ahead of print - Oct 2018 |

### Fingerprint

### Keywords

- adjacency matrix
- cospectral graphs
- spectral characterization
- pineapple graph

### Cite this

*Discrete Applied Mathematics*. https://doi.org/10.1016/j.dam.2018.10.002

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*Discrete Applied Mathematics*. https://doi.org/10.1016/j.dam.2018.10.002

**The graphs cospectral with the pineapple graph.** / Topcu, Hatice; Sorgun, Sezer; Haemers, W. H.

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

TY - JOUR

T1 - The graphs cospectral with the pineapple graph

AU - Topcu, Hatice

AU - Sorgun, Sezer

AU - Haemers, W. H.

PY - 2018/10

Y1 - 2018/10

N2 - The pineapple graph is obtained by appending q pendant edges to a vertex of a complete graph. We prove that among connected graphs, the pineapple graph is determined by its adjacency spectrum. Moreover, we determine all disconnected graphs which are cospectral with a pineapple graph. Thus we find for which values of p and q the pineapple graph is determined by its adjacency spectrum. The main tool is a recent classification of all graphs with all but three eigenvalues equal to 0 or -1 by the third author.

AB - The pineapple graph is obtained by appending q pendant edges to a vertex of a complete graph. We prove that among connected graphs, the pineapple graph is determined by its adjacency spectrum. Moreover, we determine all disconnected graphs which are cospectral with a pineapple graph. Thus we find for which values of p and q the pineapple graph is determined by its adjacency spectrum. The main tool is a recent classification of all graphs with all but three eigenvalues equal to 0 or -1 by the third author.

KW - adjacency matrix

KW - cospectral graphs

KW - spectral characterization

KW - pineapple graph

U2 - 10.1016/j.dam.2018.10.002

DO - 10.1016/j.dam.2018.10.002

M3 - Article

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -