### Abstract

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

Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 7 |

Volume | 2007-37 |

Publication status | Published - 2007 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2007-37 |

### Fingerprint

### Keywords

- Graph energy
- Strongly regular graph
- Hadamard matrix.

### Cite this

*Strongly Regular Graphs with Maximal Energy*. (CentER Discussion Paper; Vol. 2007-37). Tilburg: Operations research.

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**Strongly Regular Graphs with Maximal Energy.** / Haemers, W.H.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Strongly Regular Graphs with Maximal Energy

AU - Haemers, W.H.

N1 - Subsequently published in Linear Algebra and its Applications, 2008 Pagination: 7

PY - 2007

Y1 - 2007

N2 - The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Koolen and Moulton have proved that the energy of a graph on n vertices is at most n(1 + √n)/2, and that equality holds if and only if the graph is strongly regular with parameters (n, (n+√n)/2, (n+2√n)/4, (n+2√n)/4). Such graphs are equivalent to a certain type of Hadamard matrices. Here we survey constructions of these Hadamard matrices and the related strongly regular graphs.

AB - The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Koolen and Moulton have proved that the energy of a graph on n vertices is at most n(1 + √n)/2, and that equality holds if and only if the graph is strongly regular with parameters (n, (n+√n)/2, (n+2√n)/4, (n+2√n)/4). Such graphs are equivalent to a certain type of Hadamard matrices. Here we survey constructions of these Hadamard matrices and the related strongly regular graphs.

KW - Graph energy

KW - Strongly regular graph

KW - Hadamard matrix.

M3 - Discussion paper

VL - 2007-37

T3 - CentER Discussion Paper

BT - Strongly Regular Graphs with Maximal Energy

PB - Operations research

CY - Tilburg

ER -