The Cayley graph of a subgroup of the Burnside group B<sub>0</sub>(2, 5)
Let B<sub>0</sub>(2, 5) = (a<sub>1</sub>, a<sub>2</sub>) be the largest two-generator Burnside group of exponent five. It has the order 5<sup>34</sup>. We define an automorphism ^ under which every generator is mapped into another generator. Let C<sub>Bo</sub>(<sub>2</sub>,<sub>5</sub>)(<^) be the centralizer of in B<sub>0</sub>(2, 5). It is known that |C<sub>Bo</sub>(<sub>2</sub>,<sub>5</sub>)(^)| = 5<sup>17</sup>. We have calculated the growth function of this group relative to the minimal generating set X. As a result, the diameter and the average diameter of C<sub>Bo</sub>(<sub>2</sub>,<sub>5</sub>)(<^) are computed: (C) = 33, (C) ~ 26,1.