On local fusion graphs of finite Coxeter groups

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 ε X joined by an edge if, and only if, x ≠ 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. © de Gruyter 2013.