Fixed points for Chatterjea contractions on a metric space with a graph

In this work, we formulate Chatterjea contractions using graphs in metric spaces endowed with a graph and investigate the existence of fixed points for such mappings under two different hypotheses. We also discuss the uniqueness of the xed point. The given result here is a generalization of Chatterjea's xed point theorem from metric spaces to metric spaces endowed with a graph.