Ordering Graphs With Respect To Spectral Moments

Let G＝(V, E) be a simple and connected graph, with the vertex set V(G) and the edge set E(G).λ₁≥λ₂≥...≥λ_n are the eigenvalues in non-increasing orderof a graph G.The number (?) is called the k-th spectral moment of G,denoted by S_k.The sequence B＝(s₁(G),s₂(G),...,s_k(G)) of spectral moments is a finite sequence of invariants of a graph G.In this paper, we study the variations of the spectral moments by using transformations,and obtain the Lexicographical order of trees, unicyclic graphs and bicyclic graphs with the sequence s₄. The first three and the last three trees,unicyclic graphs and bicyclic graphs with respect to the sequence s₄ are characterized.