Nowadays, applications of networks are increased in different areas of science from biology to social science and its spread is added every day, but many issues and points are still unanswered. Finding answers to them, in addition help to understand their mathematical properties, problems in other areas, such as political are overcome. One of the issues on the networks is finding out the mean time to fixation. As the structure of graph influences on some variables of evolutionary dynamics, it is therefore logical that mean time to fixation on any graph stabilized under conditions intended to be verified. So far, much work has been done in terms of fixed and variable fitness (The fitness is independent on the outcome of a game.). An example of these efforts is the work of Dick and Whigham that they found out the mean time to fixation reduces in the star graph. Antal and Scheuring introduced an approach for the mean time to fixation that was made by Nie and Zhang to fix fitness and then by Broom for variable fitness. All these results are based on the transition probability. In this work, the relationship between the number of member of graph and mean time to fixation, for some graphs such cycle have studied analytically and numerically. These findings also demonstrate the influence of graph structure on the mean time to fixation, however it made clear whatever a graph is homogenous or close to homogenous, fixation occurs quickly. So, this approach ensures that, although the use of analytical solutions for the rest of graphs is reached to complex relationships but the simulation process was applied is capable for other graphs.
