Back

# On graceful difference labelings of disjoint unions of circuits

## Alain Hertz and Christophe Picouleau

BibTeX reference

A graceful difference labeling (gdl for short) of a directed graph $$G$$ with vertex set $$V$$ is a bijection $$f:V\rightarrow\{1,\ldots,\vert V\vert\}$$ such that, when each arc $$uv$$ is assigned the difference label $$f(v)-f(u)$$, the resulting arc labels are distinct. We conjecture that all disjoint unions of circuits have a gdl, except in two particular cases. We prove partial results which support this conjecture.

, 21 pages

### Publication

and
Open Journal of Discrete Applied Mathematics, 2(3), 38–55, 2019 BibTeX reference