Graceful labeling of digraphs—a survey

Abstract

A digraph D with p vertices and q arcs is labeled by assigning a distinct integer value g(v) from to each vertex v. The vertex values, in turn, induce a value g(u, v) on each arc (u, v) where g(u, v) = (g(v) − g(u)) (mod q + 1) If the arc values are all distinct then the labeling is called a graceful labeling of digraph. In this survey article, we have collected results that we could find interesting on graceful labeling of digraphs.

Keywords

• graceful labeling
• sequenceable group
• complete mappings
• system of simultaneous congruences
• partition