“…Using software developed at St Andrews (see Section 8 for details) we were able to calculate all the proper endomorphisms of this graph: there are 103680 Figure 1: The butterfly of these, with ranks 3, 5 and 7; the numbers of endomorphisms of each of these ranks are 25920, 51840 and 25920 respectively. Then, using GAP, we were able to determine that the endomorphism monoid of this graph is given by End(X) = G, t , where G is PΓL (2,9) and t is the transformation t =Transformation( [1,1,1,14,9,14,28,41,41,1,43,28,28,41,9,1,1,25,25,28,28,25,41,28,1,1,9,43,14,9,43,28,28,25,41,43,14,28,43,25,14,1,28,1,…”