Graceful Labelings of Directed Graphs

Abstract

A graceful labeling of a directed graph $D$ with $e$ edges is a one-to-one map $\theta :V(D)\to \{0,1,\dots ,e\}$ such that $\theta (y)–\theta (x)\mathrm{mod}(e+1)$ is distinct for each $(x,y)\in E(D)$. This paper summarizes previously known results on graceful directed graphs and presents some new results on directed paths, stars, wheels, and umbrellas.