The Graphs \(C_{11}^{(t)}\) are Graceful for \(t \equiv 0,1 \pmod 4\)

Abstract

Let \(C_n^{(t)}\) 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. Koh et al. conjectured that \(C_n^{(t)}\) is graceful if and only if \(nt \equiv 0, 3 \pmod{4}\). The conjecture has been shown true for \(n = 3, 5, 6, 7, 9, 4k\). In this paper, the conjecture is shown to be true for \(n = 11\).