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G-2018-65

On graceful difference labelings of disjoint unions of circuits

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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

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