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Defects including topological and vacancy defects have been observed in graphene during fabrication. Defects are also introduced to break the lattice symmetry of graphene and thereby obtain enhanced optoelectronic and other properties. It is important that gains in certain properties due to the presence defects are not at the expense of mechanical strength which is important in handling graphene and device fabrication. This paper presents a comprehensive study of the tensile strength and fracture strain of monolayer graphene with commonly observed topological defects and nanopores. Both molecular dynamics and the atomic-scale finite element method (AFEM) are used in this study, and the accuracy of AFEM in simulating complex topological and vacancy defects including line defects is established. It is found that the tensile strength properties have a complex dependency on the defect shape, size, and chirality. Certain defect geometries are found to be mechanically superior to other defect geometries thereby supporting the concept of topological design of graphene to optimize properties. The study also establishes AFEM as an efficient and potential tool for topological optimization of the mechanical behaviour of graphene.