  This study involves the use of Sloan Digital Sky Survey Data Release 12 (SDSS
DR12) also referred to as the Legacy Survey to investigate the influence of the
galaxy environment on the main sequence of star formation, colour bimodality
and the quenching of star formation rate. We classify the galaxies according to
the ratio of their emission lines and based on their environment (isolated and
non-isolated). We find that for $z\lesssim 0.09$, the fraction of non-isolated
galaxies is greater than isolated galaxies, whereas for $z>0.09$ the opposite
result is observed. Quenching is observed to be influenced by the environment
at $M_\star < 10^{10.7} M_{\odot}$ (mostly for the star-forming and composite
galaxies), while for $M_{\star }\geq 10^{10.7} M_{\odot}$ (mostly for Seyfert
galaxies and low-ionization nuclear emission-line regions), the effect of the
environment is very weak. We observe the decrease in the slope of the star
formation main sequence by $\sim\! 0.02$ dex and the intercept by $\sim\! 0.17$
dex for non-isolated galaxies in comparison to isolated galaxies. We also find
that star-forming, composite, Seyfert galaxies and low-ionization nuclear
emission-line regions form the evolutionary pathways, where most star-forming
galaxies ($\sim\! 60\%$) are found in the blue cloud, both composite ($\sim\!
50\%$) and Seyfert ($\sim\! 49\%$) galaxies in the green valley and
low-ionization nuclear emission-line regions ($\sim 60\%$) in the red sequence.
The study concludes that the environment in which the galaxies reside
influences the shape of the star formation main sequence, quenching and hence
colour bimodality especially for star-forming and composite galaxies while for
Seyfert and low-ionization nuclear emission-line region galaxies, there is a
mild impact.
