Abstract
The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Let \({\mathcal{T}}_{n,d}\) denote the set of trees on n vertices and diameter d, \(3\leqslant d\leqslant n-2\). Yan and Ye [Appl. Math. Lett. 18 (2005) 1046–1052] have recently determined the unique tree in \({\mathcal{T}}_{n,d}\) with minimal energy. In this article, the trees in \({\mathcal{T}}_{n,d}\) with second-minimal energy are characterized
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AMS Subject Classification: 05C50, 05C35
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Zhou, B., Li, F. On minimal energies of trees of a prescribed diameter. J Math Chem 39, 465–473 (2006). https://doi.org/10.1007/s10910-005-9047-8
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DOI: https://doi.org/10.1007/s10910-005-9047-8