Computing topological indices of drug structures provides the chemical information about the underlying topology of the drug's structures. Novel anticancer drug studies have been conducting by researches to design and produce ideal drugs. Chemical properties of these new drug candidates investigated using the simulation methods. Topological indices also have been used to investigate the chemical properties of some drug structures. Ve-degree and Ev-degree topological indices have been defined recently in chemical graph theory. In this study we evaluated the ev-degree and ye-degree topological indices of some newly defined anticancer drug candidates which are based on alkylating agent.