In this paper, we study the existence and uniqueness of fixed points for mappings with respect to a wt-distance in bmetric spaces endowed with a graph. Our results are significant, since we replace the condition of continuity of mapping with the condition of orbitally G-continuity of mapping and we consider bmetric spaces with graph instead of b-metric spaces, under which can be generalized, improved, enriched and unified a number of recently announced results in the existing literature. Additionally, we elicit all of our main results by a non-trivial example and pose an interesting two open problems for the enthusiastic readers.
