Hypercubes As Direct Products
Hypercubes As Direct Products
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DOI：
10.1137/s0895480103438358
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发表时间：
2005-04
期刊：
影响因子：
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通讯作者：
B. Brešar;W. Imrich;S. Klavžar;B. Zmazek
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文献类型：
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作者：
B. Brešar;W. Imrich;S. Klavžar;B. Zmazek
设G是连通二部图。一个保持G的二分性的对合$\alpha$称为二分的。设$G^\alpha$是由G加上$\alpha$诱导的自然完美匹配而得到的图。我们证明了k方体Qk同构于直积$G \times H$当且仅当G同构于$Q_{k-1}^\alpha$对于$Q_{k-1}$的某个二部对合$\alpha$且H=K2。
Let G be a connected bipartite graph. An involution $\alpha$ of G that preserves the bipartition of G is called bipartite. Let $G^\alpha$ be the graph obtained from G by adding to G the natural perfect matching induced by $\alpha$. We show that the k-cube Qk is isomorphic to the direct product $G \times H$ if and only if G is isomorphic to $Q_{k-1}^\alpha$ for some bipartite involution $\alpha$ of $Q_{k-1}$ and H=K2.