Super edge-graceful paths

A graph $G(V,E)$ of order $|V|=p$ and size $|E|=q$ 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 $q$ is odd and from $E$ to ${pm 1,pm 2,...,pm frac{q}{2}}$ when $q$ is even such that the induced vertex labeling $f^*$ defined by $f^*(x) = sum_{xyin E(G)}f(xy)$ over all edges $xy$ is a bijection from $V$ to ${0,pm 1,pm 2...,pm frac{p-1}{2}}$ when $p$ is odd and from $V$ to ${pm 1,pm 2,...,pm frac{p}{2}}$ when $p$ is even. indent We prove that all paths $P_n$ except $P_2$ and $P_4$ are super edge-graceful.