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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Elliot Krop
Department of Mathematics, Clayton State University, 2000 Clayton State Blvd. Morrow, georgia, 30260 USA
Electrical & Electronics Engineering

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All trees are six-cordial Keith Driscoll; Elliot Krop; Michelle Nguyen
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 1 (2017): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2017.5.1.3

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.
Co-Authors Keith Driscoll Michelle Nguyen