We have formed a complete sample of 26 low redshift (z < 0.3) giant radio galaxies (GRGs) from the WENSS survey, selected at flux densities above 1 Jy at 325 MHz. We present 10.5-GHz observations with the 100-m Effelsberg telescope of 18 sources in this sample. These observations, together with similar data of the remaining eight sources, are combined with data from the WENSS, NVSS and GB6 surveys to study the radio properties of the lobes of these sources at arcminute resolution. We investigate radio source asymmetries, equipartition energy densities in the lobes, the presence of lobe pressure evolution with redshift, the spectral age and the density of the environments of these sources. We find that the armlength asymmetries of GRGs are slightly larger than those of smaller sized 3CR radio galaxies and that these are difficult to explain as arising from orientation effects only. We also find indications that the lobes of the GRGs, despite their large sizes, are still overpressured with respect to their environment. Further, we argue that any evolution of lobe pressure with redshift in these large sources is due to selection effects. A spectral ageing analysis suggests that the GRGs in our sample are the oldest members of the group of relatively high power radio sources whose radio powers have evolved to their currently observed lower values.
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