In this paper, we introduce the concepts of weakly and partially weakly ?-admissible pair of mappings and obtain certain coincidence and fixed point theorems for classes of weakly ?-admissible contractive mappings in a b-metric space. As an application, we derive some new coincidence and common fixed point results in a b-metric space endowed with a binary relation or a graph. Moreover, an example is provided here to illustrate the usability of the obtained results.