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2011.2: On Local Fusion Graphs of Finite Coxeter Groups

2011.2: John J Ballantyne (2011) On Local Fusion Graphs of Finite Coxeter Groups.

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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 and y are not equal 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:MIMS Preprint
Uncontrolled Keywords:Group, Coxeter, Graph, Involution
Subjects:MSC 2000 > 20 Group theory and generalizations
MIMS number:2011.2
Deposited By:Dr John Ballantyne
Deposited On:09 November 2012

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