Edge-sum distinguishing labeling

We study edge-sum distinguishing labeling, a type of labeling recently introduced by Z. Tuza (2017) in context games. An ESD an $n$-vertex graph $G$ is injective mapping integers $1$ to $l$ its vertices such that for every edge, the sum on endpoints unique. If $ l$ equals $n$, we speak about canonical labeling. focus primarily structural properties this and show several classes graphs if they have or do not As application some implications these results games based also observe closely connected well-known notion magic antimagic labelings, Sidon sequences harmonious labelings.