Super edge-graceful paths

A graph $G(V,E)$ of order $\mathrm{\mid }V\mathrm{\mid }=p$ and size $\mathrm{\mid }E\mathrm{\mid }=q$ is called super edge-graceful if there is a bijection $f$ from $E$ to ${0,\pm 1,\pm 2,…,\pm \frac{q-1}{2}}$when$q$isoddandfrom$E$to${\pm 1,\pm 2,…,\pm \frac{q}{2}}$when$q$isevensuchthattheinducedvertexlabeling$f^$definedby$f^(x) = \sum_{xy\in E(G)}f(xy)$overalledges$xy$ is a bijection from $V$ to $\{0,\pm 1,\pm \mathrm{2...},\pm \frac{p-1}{2}\}$ when $p$ is odd and from $V$ to $\{\pm 1,\pm 2,\mathrm{.}\mathrm{.}\mathrm{.},\pm \frac{p}{2}\}$ when $p$ is even. \indent We prove that all paths $P_n$ except $P_2$ and $P_4$ are super edge-graceful.