Xor-Magic图

J. Siehler
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引用次数: 0

摘要

如果一个有2n个顶点的连通图可以用不同的n位二进制数标记,并且每个顶点的标记等于相邻顶点上标记的逐位xor,则定义为xor-magic。我们展示了在2n个顶点上对于每一个n大于或等于2的顶点至少有一个3-正则x -幻图。我们对8点和16点上的3正则x -幻图进行了分类,并给出了32点上的3正则x -幻图的多个例子,其中包括著名的Dyck图。
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Xor-Magic Graphs
Abstract A connected graph on 2n vertices is defined to be xor-magic if the vertices can be labeled with distinct n-bit binary numbers in such a way that the label at each vertex is equal to the bitwise xor of the labels on the adjacent vertices. We show that there is at least one 3-regular xor-magic graph on 2n vertices for every n ⩾ 2. We classify the 3-regular xor-magic graphs on 8 and 16 vertices, and give multiple examples of 3-regular xor-magic graphs on 32 vertices, including the well-known Dyck graph.
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