Extensions of Banach contraction principle have mainly been obtained either by generalizing the domain or by extending the contractive condition on the mappings or extending the range of the mappings. The existence of fixed points of maps in the setup of partially ordered metric spaces has been studied by Ran and Reurings Ran and Reurings. The study of fixed point theory endowed with a graph occupies a prominent place in many aspects. Echenique Echenique studied fixed point theory by using the graphic structure. The chapter provides the definitions and results for coincidence and common fixed points of multivalued mappings that satisfying the weakly commuting condition. Bojor Bojor proved fixed point theorems for Reich type contractions on metric spaces with a graph.