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Let $S(G)=(S_0(G),S_1(G),...,S_{n-1}(G))$ be the sequence of spectral moments of $G$. For two graphs $G_1$ and $G_2$, we have $G_1\\prec_sG_2$ if $S_i(G_1)=S_i(G_2)  (i=0,1,...,k-1)$ and $S_k(G_1)<S_k(G_2)$ for some $k\\in {1,2,...,n-1}$. Denote by $\\mathscr{G}_n^k$ the set of connected $n$-vertex graphs with $k$ cut edges. 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Call the number $S_k(G):=\\sum_{i=1}^{n}\\lambda_{i}^k(G) (k=0,1,...,n-1)$ the $k$th spectral moment of $G$. Let $S(G)=(S_0(G),S_1(G),...,S_{n-1}(G))$ be the sequence of spectral moments of $G$. For two graphs $G_1$ and $G_2$, we have $G_1\\prec_sG_2$ if $S_i(G_1)=S_i(G_2)  (i=0,1,...,k-1)$ and $S_k(G_1)<S_k(G_2)$ for some $k\\in {1,2,...,n-1}$. Denote by $\\mathscr{G}_n^k$ the set of connected $n$-vertex graphs with $k$ cut edges. 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