### Abstract

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

Pages (from-to) | 219-228 |

Journal | Linear Algebra and its Applications |

Volume | 539 |

DOIs | |

Publication status | Published - 15 Feb 2018 |

### Fingerprint

### Keywords

- Determined by spectrum
- Eigenvalues
- Godsil–McKay switching
- Graph
- Johnson association scheme
- Kneser graph

### Cite this

*Linear Algebra and its Applications*,

*539*, 219-228. https://doi.org/10.1016/j.laa.2017.11.011

}

*Linear Algebra and its Applications*, vol. 539, pp. 219-228. https://doi.org/10.1016/j.laa.2017.11.011

**Cospectral mates for the union of some classes in the Johnson association scheme.** / Cioabă, Sebastian M.; Haemers, Willem H.; Johnston, Travis; McGinnis, Matt.

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

TY - JOUR

T1 - Cospectral mates for the union of some classes in the Johnson association scheme

AU - Cioabă, Sebastian M.

AU - Haemers, Willem H.

AU - Johnston, Travis

AU - McGinnis, Matt

PY - 2018/2/15

Y1 - 2018/2/15

N2 - Let n≥k≥2 be two integers and S a subset of {0,1,…,k−1}. The graph JS(n,k) has as vertices the k-subsets of the n-set [n]={1,…,n} and two k-subsets A and B are adjacent if |A∩B|∈S. In this paper, we use Godsil–McKay switching to prove that for m≥0, k≥max(m+2,3) and S={0,1,…,m}, the graphs JS(3k−2m−1,k) are not determined by spectrum and for m≥2, n≥4m+2 and S={0,1,…,m} the graphs JS(n,2m+1) are not determined by spectrum. We also report some computational searches for Godsil–McKay switching sets in the union of classes in the Johnson scheme for k≤5.

AB - Let n≥k≥2 be two integers and S a subset of {0,1,…,k−1}. The graph JS(n,k) has as vertices the k-subsets of the n-set [n]={1,…,n} and two k-subsets A and B are adjacent if |A∩B|∈S. In this paper, we use Godsil–McKay switching to prove that for m≥0, k≥max(m+2,3) and S={0,1,…,m}, the graphs JS(3k−2m−1,k) are not determined by spectrum and for m≥2, n≥4m+2 and S={0,1,…,m} the graphs JS(n,2m+1) are not determined by spectrum. We also report some computational searches for Godsil–McKay switching sets in the union of classes in the Johnson scheme for k≤5.

KW - Determined by spectrum

KW - Eigenvalues

KW - Godsil–McKay switching

KW - Graph

KW - Johnson association scheme

KW - Kneser graph

U2 - 10.1016/j.laa.2017.11.011

DO - 10.1016/j.laa.2017.11.011

M3 - Article

VL - 539

SP - 219

EP - 228

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -