Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070320180901$ b-(varphi, Gamma)-$graphic contraction on metric space endowed with a graph245250543269ENSh. MirzaeeDepartment of Mathematics, Karaj Branch, Islamic Azad University, Alborz, IranM. Eshaghi GordjiDepartment of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranJournal Article20180521In this paper, we introduce the $ b-(varphi, Gamma)-$graphic contraction on metric space endowed with a graph so that $(M,delta)$ is a metric space, and $V(Gamma)$ is the vertices of $Gamma$ coincides with $M$. We aim to obtain some new fixed-point results for such contractions. We give an example to show that our results generalize some known results.http://jlta.iauctb.ac.ir/article_543269_af9dfc9bce7ff45a030476a15eae4138.pdf