Ballantyne, John J
(2013)
*On Local Fusion Graphs of Finite Coxeter Groups.*
Journal of Group Theory, 16 (4).
pp. 595-617.
ISSN 1749-9097

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## Abstract

Given a finite group G and G-conjugacy class of involutions X, the local fusion graph F(G,X) has X as its vertex set, with x,y in X joined by an edge if, and only if, x is not equal to y and the product xy has odd order. In this note we investigate such graphs when G is a finite Coxeter group, addressing questions of connectedness and diameter. In particular, our results show that local fusion graphs may have an arbitrary number of connected components, each with arbitrarily large diameter.

Item Type: | Article |
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Uncontrolled Keywords: | Group, Coxeter, Graph, Involution |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations |

Depositing User: | Dr John Ballantyne |

Date Deposited: | 19 Sep 2014 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2178 |

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