# Super edge-graceful paths - Mathematics > Combinatorics

Abstract: A graph $GV,E$ of order $|V|=p$ and size $|E|=q$ is called superedge-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 $f^*x = \sum {xy\in EG}fxy$ over all edges $xy$ is a bijectionfrom $V$ 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 provethat all paths $P n$ except $P 2$ and $P 4$ are super edge-graceful.

Author: Sylwia Cichacz, Dalibor Froncek, Wenjie Xu

Source: https://arxiv.org/