Three periodic structures based on arrays of graphene-like nanocluster have been proposed and their plasmonic response has been investigated. In the first step, plasmonic response of each periodic structure has been investigated using the hybridization diagram for a proposed single unit cell. In the second step, according to obtained results, appropriate applications for each structure have been introduced. The study is divided into three sections. In the first section, we have considered a periodic array of triangular-shaped nanoparticles to form a graphene-like nanocluster. This configuration shows considerable capabilities to act as a nanoscale waveguide. Alternatively, in the second section, we have replaced triangular nanoparticles with nanospheres. Results of this configuration show considerable enhancements in optical forces and hence, represent it as an acceptable candidate for tweezing and optical manipulations. Finally, we have replaced nanospheres with ring nanoparticles in each node of such a similar nanocluster. This change leads to create states of plasmonic resonances in spectral response, which is sensitive to surrounding medium and can be used as a sensing tool to detect medium perturbations.