  We study a two terminal electronic conductance through an AB$_2$ ring which
is an example of the family of itinerant geometrically frustrated electronic
systems. These systems are characterized by the existence of localized states
with nodes in the probability density. We show that such states lead to
distinct features in the conductance. For zero magnetic flux, the localized
states act as a filter of the zero frequency conductance peak, if the contact
sites have hopping probability to sites which are not nodes of the localized
states. For finite flux, and in a chosen orthonormal basis, the localized
states have extensions ranging from two unit cells to the complete ring, except
for very particular values of magnetic flux. The conductance exhibits a zero
frequency peak with a dip which is a distinct fingerprint of the variable
extension of these localized states.
