On (Super) Vertex-Graceful Labeling Of Graphs

Abstract

In the paper, we discuss properties of the (super) vertex-graceful labeling of cycle \(C_n\), crown graph \(C_n \odot K_1\), and generalized crown graph \(C_n \odot K_{1,t}\), and prove that \(C_n\), \(C_{n} \odot K_1\), and \(C_n \odot K_{1,t}\) are vertex-graceful if \(n\) is odd; \(C_n\) is super vertex-graceful if \(n \neq 4, 6\); and \(C_{n} \odot K_1\) is super vertex-graceful if \(n\) is even. Moreover, we propose two conjectures on (super)vertex-graceful labeling.