On the minimal energy of trees with a given diameter
On the minimal energy of trees with a given diameter
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DOI：
10.1016/j.aml.2004.11.001
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发表时间：
2005-09
期刊：
影响因子：
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通讯作者：
Weigen Yan;Luzhen Ye
中科院分区：
文献类型：
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作者：
Weigen Yan;Luzhen Ye
图的能量定义为图的所有特征值的绝对值之和。 F. 张，H. Li [关于具有最小能量的无环共轭分子，离散应用。 数学。 92 (1999) 71–84] 描述了具有最小和第二最小能量的完美匹配的树，这解决了 I. Gutman 提出的猜想 [非循环共轭分子，树及其能量，J. Math. 92 (1999) 71–84] 化学。 1（1987）123-143]。在这封信中，对于给定的正整数 d，我们用直径至少为 d 的最小能量来表征树。作为推论，我们还用直径至少为 d 的最小 Hosoya 指数来表征树。
The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. F. Zhang, H. Li [On acyclic conjugated molecules with minimal energies, Discrete Appl. Math. 92 (1999) 71–84] characterized the trees with a perfect matching having the minimal and the second minimal energies, which solved a conjecture proposed by I. Gutman [Acyclic conjugated molecules, trees and their energies, J. Math. Chem. 1 (1987) 123–143]. In this letter, for a given positive integer d we characterize the tree with the minimal energy having diameter at least d. As a corollary, we also characterize the tree with the minimal Hosoya index having diameter at least d.