A subset of vertices in a graph G is called a maximum dissociation set if it induces a subgraph with vertex degree at most 1 and the subset has maximum cardinality. The dissociation number of G, denoted by \(\psi (G)\), is the cardinality of a maximum dissociation set. A subcubic tree is a tree of maximum degree at most 3. In this paper, we give the lower and upper bounds on the dissociation number in a subcubic tree of order n and show that the number of maximum dissociation sets of a subcubic tree of order n and dissociation number \(\psi \) is at most \(1.466^{4n-5\psi +2}\).

中文翻译：

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亚立方树中的最大解离集

如果图G中的顶点子集归纳出顶点度数至多为 1 的子图并且该子集具有最大基数，则该子集称为最大解离集。G的解离数用\(\psi (G)\)表示，是最大解离集的基数。次立方树是最大度数最多为 3 的树。本文给出了n阶次立方树中解离数的下界和上限，并表明阶数次立方树的最大解离集数n和解离数\(\psi \)至多为\(1.466^{4n-5\psi +2}\)。