In this paper we consider optimal edge colored fan graph and wheel graph. On those graph we could obtain rainbow path or cycle, that is path or cycle whose all edges have different colors. We show that there is optimal edge coloring rules for fan graph and wheel graph such that with these coloring we can obtain rainbow cycles with length 3, 4, ⋯, n, with n denotes edge chromatic number and rainbow paths with length 1, 2, ⋯, n. © 2018 Author(s).