科研之友
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摘要
The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the graph. A k-subdivision graph G(e)(k) is a graph obtained from a graph C by subdividing a cut, edge e of G by k times. In this paper, we present a new method to compare the energies of two k-subdivision bipartite graphs of the same order. As an application of this method, we determine the first largest to the [n-7/2](th) largest energy trees of order n for n >= 31 (which is a partial result on a conjecture proposed by Andriantiana in [1]), and also give a simplified proof of the conjecture on the fourth maximal energy tree.
