  A group $G$ has a Frobenius graphical representation (GFR) if there is a
simple graph $\varGamma$ whose full automorphism group is isomorphic to $G$ and
it acts on vertices as a Frobenius group. In particular, any group $G$ with GFR
is a Frobenius group and $\varGamma$ is a Cayley graph. The existence of an
infinite family of groups with GFR whose Frobenius kernel is a non-abelian
$2$-group has been an open question. In this paper, we give a positive answer
by showing that the Higman group $A(f,q_0)$ has a GFR for an infinite sequence
of $f$ and $q_0$.
