Abstract
The authors obtain a new property of the n-dimensional binary undirected de Bruijn graph UB(n) for n ≥ 4, namely, there is a vertex x such that for any other vertex y there exist at least two internally disjoint paths of length at most n - 1 between x and y in UB(n). The result means that the (n - 1, 2)-dominating number of UB(n) is equal to one if n ≥ 4.
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Project supported by the National Natural Science Foundation of China (No. 19971086 and 19871040) and the Jiangsu Provincial Natural Science Foundation of China.
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Xu, J., Lu, C. & Zhang, K. A New Property of Binary Undirected de Bruijn Graphs. Chin. Ann. of Math. 21, 39–42 (2000). https://doi.org/10.1007/BF02731956
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DOI: https://doi.org/10.1007/BF02731956