  In this paper, we determine the diameter of the commuting involution graphs
of special and general linear groups over an arbitrary field. It turns out that
our results also determine the diameter for certain projective special linear
groups over finite fields. Moreover, we find the diameter of the commuting
graphs of general linear groups on the set of all involutions over a field of
characteristic 2, which completes the diameter of general linear groups on the
set of all involutions. As an application, we classify the structure of the
four-dimensional linear groups over finite fields according to the distance
from a fixed involution.
