The Energy Of Tree With A Given Diameter And Hyperenergetic Graph

The totalπ-electron energy is one of the most useful quantum-chemical characteristics of a conjugated molecule that can be obtained by means of the Huckel molecular-orbital (HMO) theory.Until the end of the 1970s, numerous mathematical results were obtained in the theory of HMO totalπ-electron energy.The energy of G is the sum of the absolute vlaues of the eigenvalues of G.It is of great importance to study the extramal energy of G. In this thesis we obtained the following conclutions.Firstly, the energy of B_n,d is a strictly increasing function of the diameter d and the energy of T(n,d;n-d-k-1,0,0,…,k) is a strictly increasing function of k which is the number of pendent vertices adjacent to v_d. Secondly ,the tree T_n^d(t)with diameter d and all the pendent vertices adjacent to unique v, are discussed . Also the energy of T_n^d(t) is studied. Thirdly ,we give the tree with third minimal energy with a given diameter. At last we studied the hyperenergetic graph and give a kind of graph with hyperenergetic.All the results in the thesis are deduced in the following way:Firstly,we compare the matching numbers of the graphs involved;Secondly,we compare the absolute values of the coefficients of the characteristic polynomials of the graphs.