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This research aims to investigate a novel coincidence point (cp) of generalized multivalued contraction (gmc) mapping involved a directed graph in  b -metric spaces (b-ms). An example and some corollaries are derived to strengthen our main theoretical results. We end the manuscript with two important applications, one of them is interested in finding a solution to the system of nonlinear integral equations (nie) and the other one relies on the existence of a solution to fractional integral equations (fie).

New coincidence point results for generalized graph-preserving multivalued mappings with applications