Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767624 
Title:  Affine Coxeter groups, involution classes and commuting involution graphs  
Author:  Sbeiti Clarke, Amal 
ISNI:
0000 0004 7660 4273


Awarding Body:  Birkbeck, University of London  
Current Institution:  Birkbeck (University of London)  
Date of Award:  2018  
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Abstract:  
For a group G and X a subset of G the commuting graph of G on X, denoted C(G,X), is the graph whose vertex set is X where there is an edge joining x,y Є X whenever x commutes with y and x≠y. If the elements of X are involutions, then C(G,X) is called a commuting involution graph. In this thesis, we investigate conjugacy classes of involutions, studying the connectedness of the commuting involution graph and determining the size of the diameter of the connected C(G,X), where X is a conjugacy class of involutions of G and G is an affine Coxeter group. We show that if G is of type ~ Cn, ~Bn or ~Dn and C(G,X) is connected, then Diam C(G;X) is at most n+2. If G is of type ~G2, then C(G,X) is disconnected. If G is of type ~ F4, then C(G,X) is connected when X is a conjugacy class of (r2r3)2 or r3r5. Otherwise, it is disconnected. Finally, we examine the connectedness of C(W,X) where W is an arbitrary Coxeter group, R is its set of simple reflections, and X = RW. In this case we call C(W,X) the commuting reflection graph of W.


Supervisor:  Not available  Sponsor:  Not available  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.767624  DOI:  Not available  
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