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Super Edge-graceful Labelings of Kites

Alexander Clifton1, Abdollah Khodkar2
1Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139
2University of West Georgia Department of Mathematics University of West Georgia Carrollton, GA 30118

Abstract

A graph \(G\) with vertex set \(V\) and edge set \(E\) is called super edge-graceful if there is a bijection \(f\) from \(E\) to \(\{0, \pm 1, \pm 2, \dots, \pm (|E| – 1)/2\}\) when \(|E|\) is odd and from \(E\) to \(\{\pm1, \pm2, \dots, \pm|E|/2\}\) when \(|E|\) is even, such that the induced vertex labeling \(f^*\) defined by \(f^*(u) = \sum f(uv)\) over all edges \(uv\) is a bijection from \(V\) to \(\{0, \pm 1, \pm 2, \dots, \pm (|V| – 1)/2\}\) when \(|V|\) is odd and from \(V\) to \(\{\pm1, \pm2, \dots, \pm|V|/2\}\) when \(|V|\) is even. A kite is a graph formed by merging a cycle and a path at an endpoint of the path. In this paper, we prove that all kites with \(n \geq 5\) vertices, \(n \neq 6\), are super edge-graceful.