Alain Hertz
and Christophe Picouleau
Article (2019)
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Abstract
A graceful difference labeling (gdl for short) of a directed graph G with vertex set V is a bijection f:V → {1,...,|V|} 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.
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| Department: | Department of Mathematics and Industrial Engineering |
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| Research Center: | GERAD - Research Group in Decision Analysis |
| PolyPublie URL: | https://publications.polymtl.ca/9457/ |
| Journal Title: | Open Journal of Discrete Applied Mathematics (vol. 2, no. 3) |
| Publisher: | PSR Press |
| DOI: | 10.30538/psrp-odam2019.0021 |
| Official URL: | https://doi.org/10.30538/psrp-odam2019.0021 |
| Date Deposited: | 16 Aug 2023 14:33 |
| Last Modified: | 11 Jan 2026 06:58 |
| Cite in APA 7: | Hertz, A., & Picouleau, C. (2019). On graceful difference labelings of disjoint unions of circuits. Open Journal of Discrete Applied Mathematics, 2(3), 38-55. https://doi.org/10.30538/psrp-odam2019.0021 |
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