  About 6% of Radio Galaxies (RG) can reach linear sizes larger than 0.7 Mpc,
and are then classified as Giant Radio Galaxies (GRG). The conditions that make
possible the formation of such big structures is still not clear - either core
accretion properties or environmental factors. Recent studies have shown that
GRG can be up to four times more abundant in hard X-ray selected (i.e. from
INTEGRAL/IBIS and Swift/BAT at >20 keV) RG samples. Moreover, a high fraction
of young radio sources found in their cores suggests a recently restarted
activity, as suggested from the discrepancy between the measured jet and lobes
power, with respect to the one expected from core X-ray luminosity. Here we
present a radio morphological study of a sample of 15 hard X-ray selected GRG,
discussing low-frequency images from our GMRT campaign complemented with others
from the literature: among them, 7/15 show evidence of restarted radio activity
either in the form of double-double/X-shaped morphology, or as a cocoon
emission embedding more recent jets. This, together with the objects from this
sample already found hosting a young radio source in their core, suggests that
at least 13 over 15 of these hard X-ray selected GRG show features which are
consistent with the possibility of restarted radio activity.
