Merrifield-Simmons index and minimum Number of Independent Sets in Short Trees

Merrifield-Simmons index and minimum Number of Independent Sets in Short Trees
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发表时间：
2013
期刊：
Ars Comb.
影响因子：
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通讯作者：
A. Frendrup;A. S. Pedersen;A. A. Sapozhenko-A.;P. Vestergaard
A. Frendrup;A. S. Pedersen;A. A. Sapozhenko-A.;P. Vestergaard
中科院分区：
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文献类型：
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作者：
A. Frendrup;A. S. Pedersen;A. A. Sapozhenko-A.;P. Vestergaard

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在Ars Comb. 84(2007)， 85-96中，Pedersen和Vestergaard提出了确定直径为d的定阶树中独立集个数下界的问题。本文给出了直径为d≤5的树的渐近完全解。下界是5我们给出了极值树的结构。对连通图进行了推广。
In Ars Comb. 84 (2007), 85–96, Pedersen and Vestergaard posed the problem of determining a lower bound for the number of independent sets in a tree of fixed order and diameter d. Asymptotically, we give here a complete solution for trees of diameter d ≤ 5. The lower bound is 5 and we give the structure of the extremal trees. A generalization to connected graphs is stated.