Mačaj, Martin and Širáň, Jozef
(2010).
*Linear Algebra and its Applications*, 432(9) pp. 2381–2398.

DOI (Digital Object Identifier) Link: | http://dx.doi.org/10.1016/j.laa.2009.07.018 |
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## Abstract

In the degree-diameter problem, the only extremal graph the existence of which is still in doubt is the Moore graph of order 3250, degree 57 and diameter 2. It has been known that such a graph cannot be vertex-transitive. Also, certain restrictions on the structure of the automorphism group of such a graph have been known in the case when the order of the group is even. In this paper we further investigate symmetries and structural properties of the missing Moore (57, 2)-graph(s) with the help of a combination of spectral, group-theoretic, combinatorial, and computational methods. One of the consequences is that the order of the automorphism group of such a graph is at most 375.

Item Type: | Journal Article |
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Copyright Holders: | 2009 Elsevier Inc. |

ISSN: | 0024-3795 |

Keywords: | Moore graphs; spectral graph theory; rational representations |

Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics Mathematics, Computing and Technology |

Item ID: | 23259 |

Depositing User: | Jozef Širáň |

Date Deposited: | 24 Sep 2010 14:36 |

Last Modified: | 15 Jan 2016 14:56 |

URI: | http://oro.open.ac.uk/id/eprint/23259 |

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