The　nullity　of　a　graph　G,　denoted　by　(Formula　presented.)　,　is　the　multiplicity　of　the　eigenvalue　zero　of　its　adjacency　matrix.　In　this　paper,　we　determine　all　graphs　with　(Formula　presented.)　,　where　(Formula　presented.)　,　and　(Formula　presented.)　,　(Formula　presented.)　,　(Formula　presented.)　,　and　(Formula　presented.)　are　the　vertex　number,　edge　number,　matching　number,　and　the　number　of　connected　components　of　G,　respectively.　©　2016,　Rula　et　al.