## All trees are 6-cordial

dc.contributor.author | Elliot Krop | |

dc.contributor.author | Keith Driscoll | |

dc.contributor.author | Michelle Nguyen | |

dc.date.accessioned | 2024-05-08T19:07:27Z | |

dc.date.available | 2024-05-08T19:07:27Z | |

dc.description.abstract | For any integer $k>0$, a tree $T$ is $k$-cordial if there exists a labeling of the vertices of $T$ by $\mathbb{Z}_k$, inducing edge-weights as the sum modulo $k$ of the labels on incident vertices to a given edge, which furthermore satisfies the following conditions: \begin{enumerate} \item Each label appears on at most one more vertex than any other label. \item Each edge-weight appears on at most one more edge than any other edge-weight. \end{enumerate} Mark Hovey (1991) conjectured that all trees are $k$-cordial for any integer $k$. Cahit (1987) had shown earlier that all trees are $2$-cordial and Hovey proved that all trees are $3,4,$ and $5$-cordial. We show that all trees are six-cordial by an adjustment of the test proposed by Hovey to show all trees are $k$-cordial. | |

dc.identifier | http://www.ejgta.org/index.php/ejgta | |

dc.identifier.uri | https://hdl.handle.net/20.500.12951/442 | |

dc.title | All trees are 6-cordial | |

dc.type | Journal Article, Academic Journal | |

dcterms.bibliographicCitation | Electronic Journal of Graph Theory and Applications 5(1), 21-35, (Spring 2017) |