A set of vertices in a graph is a total dominating set of if every vertex of is adjacent to some vertex in . The minimum cardinality of a total dominating set of is the total domination number of . The graph is total domination edge-critical, or , if for every edge in the complement of , . If is and , we say that is . In this paper, we show that every graph with and has a Hamilton cycle.

中文翻译：

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图的哈密顿性

图中的一组顶点是的总控制集，如果的每个顶点都与中的某个顶点相邻。共支配集的最小基数为总控制数的。该图是总控制边临界的，如果为的补码中的每个边，则为， 。如果是和，我们说是。在本文中，我们显示了每个具有 和 有一个汉密尔顿周期。