Regarding the vector metric space introduced by Cevik and Altun, we first introduce the concept of a graphical vector metric space and then define several topological notions therein such as 3-Dedekind complete Riesz spaces, vectorially G-continuous mappings, vectorially G-proximal mappings, vector P-property. Then some best prox- consequences and an illustrative example are also provided to support our definitions similar researches is that it can also encompass all of those previously introduced by
