Summary: Let \(C_{n}\) denote the cycle with \(n\) vertices and \(C_{n}^{(t)}\) denote the graphs consisting of \(t\) copies of \(C_{n}\) with a vertex in common. K. M. Koh, D. G. Rogers, P. Y. Lee and C. W. Toh [Nanta Math. 12, 133–136 (1979; Zbl 0428.05048)] conjectured that \(C_{n}^{(t)}\) is graceful if and only if \(nt \equiv 0,3 \pmod 4\). The conjecture has been shown true for \(n = 3, 5, 6, 7, 9, 11, 4k\). In this paper, the conjecture is shown to be true for \(n = 13\).