On the spectral moment of graphs with K cut edges

Abstract

Let A(G) be the adjacency matrix of a graph G with λ1(G), λ2(G),..., λn(G) its eigenvalues in non-increasing order. Call the number Sk(G):= ∑ni=1 λki (G) (k = 0, 1,..., n - 1) the kth spectral moment of G. Let S(G) = (S0(G), S1(G),..., Sn-1(G)) be the sequence of spectral moments of G. For two graphs G1 and G2, we have G1 ≺s G2 if Si(G1) = Si(G2) for i = 0, 1,..., k-1 and Sk(G1) < Sk(G2) for some k ∈ {1, 2,..., n - 1}. Denote by Gkn the set of connected n-vertex graphs with k cut edges. In this paper, the first, the second, the last and the penultimate graphs, in the S-order, are determined among Gkn, respectively.