A series of trees with the first $\lfloor\frac{n-7}{2}\rfloor$ largest energies

Details A series of trees with the first $\lfloor\frac{n-7}{2}\rfloor$ largest energies A series of trees with the first $\lfloor\frac{n-7}{2}\rfloor$ largest energies

2011-11-09

arxiv.org/abs/1111.2084v1

Mathematics

Combinatorics

Scientific paper

The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the graph. In this paper, we present a new method to compare the energies of two $k$-subdivision bipartite graphs on some cut edges. As the applications of this new method, we determine the first $\lfloor\frac{n-7}{2}\rfloor$ largest energy trees of order $n$ for $n\ge 31$, and we also give a simplified proof of the conjecture on the fourth maximal energy tree.

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