A note on test elements for monomorphisms of free groups

A word in a group is called a test element if any endomorphism fixing it is necessarily an automorphism. In this note, we give a sufficient condition in geometry to construct test elements for monomorphisms of a free group, by using the Whitehead graph and the action of the free group on its Cayley graph. 9 pages, 4 figures. Published in the journal of Groups, Complexity, Cryptology