The Minimal Energies Of Trees With A Given Maximum Degree

The energy of a graph is defined as the sum of absolute values of its eigenvalues. To find the extremal energies of a class of graphs or to give an order of graphs with respect to energy is one of the most important topics in Chemical Graph Theory. From the definition of energy, energy of of a graph can be obtained from the spectrum of the graph. On the other hand, for acyclic graphs, the energy of a graph can be expressed as a monotomically increasing function of mathing numbers of the graph, which provides us another way of studing energy, specially ordering graphs with respect to energy.Let T_n denote the set of trees with n vertices, and T_n~△the set of trees with n vertices and maximum degree△.In [21], W. Lin and X. Guo determined the trees in T_n~△with maximal energy for 3≤△≤n - 2, and the tree in T_n~△with minimal energy for [(n+1)/3]≤△(T)≤n - 2.In this paper, we determine the trees in T_n~△with minimal energy for...