{"paper":{"title":"On the spectral moment of graphs with $k$ cut edges","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huihui Zhang, Shuchao Li","submitted_at":"2012-09-12T09:09:33Z","abstract_excerpt":"Let $A(G)$ be the adjacency matrix of a graph $G$ with $\\lambda_{1}(G)$, $\\lambda_{2}(G)$, ..., $\\lambda_{n}(G)$ being its eigenvalues in non-increasing order. 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. In this p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2528","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}