The distance energy of a simple connected graph G is defined as the sum absolute values its eigenvalues. In this paper, we mainly give positive answer to conjecture clique trees proposed by Lin et al. (2015) [16].

Rotation distance between trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. In the case of ordered rooted trees, we show that the rotation distance between two ordered trees is fixed-parameter tractable, in the parameter, k, the rotation distance. The proof relies on the kern...