Not all partial cubes are ?-graceful
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Date
2020
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Abstract
It is shown that the graph obtained by merging two vertices of two 4-cycles is not a ?-graceful partial cube, thus answering in the negative a question by Bre�ar and Klav�ar from Bre�ar and Klav�ar (2006), who asked whether every partial cube is ?-graceful. � 2020 Elsevier B.V.
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Graceful labelings; Partial cubes; Ringel�Kotzig conjecture; Trees
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2