## Cayley graphs and metric spaces: An
investigation of groups and their generators

### Claire Ihlendorf and Erin Kelly

A choice of generators for a discrete group determines a Cayley
graph, and hence a metric space structure, for the group. This paper
investigates the relationship between the group operation and the
metric. In particular this paper formulates, and proves for some
classes of groups, the following conjecture: for a finite group of
even order, generated by two or fewer generators, there exists a
Cayley graph that is constructed using no more than two generators
and in which the element farthest from the identity has order two.
(advisor Peter Haskell)