Koolen, J., Moulton, V. ORCID: https://orcid.org/0000-0001-9371-6435 and Stevanovic, D.
(2004)
*The structure of spherical graphs.*
European Journal of Combinatorics, 25 (2).
pp. 299-310.
ISSN 0195-6698

## Abstract

A spherical graph is a graph in which every interval is antipodal. Spherical graphs are an interesting generalization of hypercubes (a graph G is a hypercube if and only if G is spherical and bipartite). Besides hypercubes, there are many interesting examples of spherical graphs that appear in design theory, coding theory and geometry e.g., the Johnson graphs, the Gewirtz graph, the coset graph of the binary Golay code, the Gosset graph, and the Schläfli graph, to name a few. In this paper we study the structure of spherical graphs. In particular, we classify a subclass of these graphs consisting of what we call the strongly spherical graphs. This allows us to prove that if G is a triangle-free spherical graph then any interval in G must induce a hypercube, thus providing a proof for a conjecture due to Berrachedi, Havel and Mulder.

Item Type: | Article |
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Additional Information: | In memory of Jaap Seidel |

Faculty \ School: | Faculty of Science > School of Computing Sciences |

Depositing User: | Vishal Gautam |

Date Deposited: | 09 Jun 2011 17:55 |

Last Modified: | 24 Oct 2022 02:33 |

URI: | https://ueaeprints.uea.ac.uk/id/eprint/22623 |

DOI: | 10.1016/S0195-6698(03)00116-1 |

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