All trees are six-cordial
نویسندگان
چکیده
For any integer k > 0, a tree T is k-cordial if there exists a labeling of the vertices of T by Zk, inducing edge-weights as the sum modulo k of the labels on incident vertices to a given edge, which furthermore satisfies the following conditions: 1. Each label appears on at most one more vertex than any other label. 2. Each edge-weight appears on at most one more edge than any other edge-weight. 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.
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ورودعنوان ژورنال:
- EJGTA
دوره 5 شماره
صفحات -
تاریخ انتشار 2017