Not all partial cubes are $\Theta$-graceful
Combinatorics
2020-01-07 v2
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\v{s}ar and Klav\v{z}ar from [1], who asked whether every partial cube is -graceful.
Cite
@article{arxiv.1809.05320,
title = {Not all partial cubes are $\Theta$-graceful},
author = {Nathann Cohen and Matjaž Kovše},
journal= {arXiv preprint arXiv:1809.05320},
year = {2020}
}