The Super Vertex-Graceful Labeling Of Graphs

Abstract

Lee and Wei defined super vertex-graceful labeling in 2006. In this paper, the generalized Butterfly Graph \(B_{n}^t\) and \(C_n^{(t)}\) graph are discussed. The generalized butterfly Graph \(B_{n}^t\) is super vertex-graceful when \(t\) (\(t > 0\)) is even, \(B_{n}^0\) is super vertex-graceful when \(n \equiv 0, 3 \pmod{4}\); For \(C_3^{(t)}\), there are: \(C_3^{(t)}\) is super vertex-graceful if and only if \(t = 1, 2, 3, 5, 7\). Moreover, we propose two conjectures on super vertex-graceful labeling.