Integrated star formation rate (SFR) and specific star formation rate (SFR/M*), derived from the spectroscopic data obtained by the Sloan Digital Sky Survey (SDSS) data release 4 (DR4), are used to show that the star formation activity in galaxies (Mr ≤ −20.5) found on the outskirts (1–2r200) of some nearby clusters (0.02 ≤ z ≤ 0.15) is enhanced. By comparing the mean SFR of galaxies in a sample of clusters with at least one starburst galaxy (log SFR/M* ≥ −10 yr−1 and SFR ≥ 10 M⊙ yr−1) to a sample of clusters without such galaxies (‘comparison’ clusters), we find that despite the expected decline in the mean SFR of galaxies towards the cluster core, the SFR profile of the two samples is different. Compared to the clusters with at least one starburst galaxy on their outskirts, the galaxies in the ‘comparison’ clusters show a lower mean SFR at all radius (≤3r200) from the cluster centre. Such an increase in the SFR of galaxies is more likely to be seen in dynamically unrelaxed (σv ≳ 500 km s−1) clusters. It is also evident that these unrelaxed clusters are currently being assembled via galaxies falling in through straight filaments, resulting in high velocity dispersions. On the other hand, ‘comparison’ clusters are more likely to be fed by relatively low density filaments. We find that the starburst galaxies on the periphery of clusters are in an environment of higher local density than other cluster galaxies at similar radial distances from the cluster centre. We conclude that a relatively high galaxy density in the infalling regions of clusters promotes interactions amongst galaxies, leading to momentary bursts of star formation. Such interactions play a crucial role in exhausting the fuel for star formation in a galaxy, before it is expelled due to the environmental processes that are operational in the dense interiors of the cluster.