All trees are six-cordial

Keith Driscoll, Elliot Krop, Michelle Nguyen
2017 Electronic Journal of Graph Theory and Applications  
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 a labeling on the edges with edge-weights found by summing the labels on vertices incident to a given edge modulo $k$ so that each label appears on at most one more vertex than any other and each edge-weight appears on at most one more edge than any other. We prove that all trees are six-cordial by an adjustment of the test proposed by Hovey (1991) to show all trees are
more » ... show all trees are $k$-cordial.
doi:10.5614/ejgta.2017.5.1.3 fatcat:mog45n63nrctbcohim6x3dpcgy