{"paper":{"title":"On the second largest distance eigenvalue of a graph","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Xue, Litao Guo, Ruifang Liu","submitted_at":"2015-04-16T13:39:08Z","abstract_excerpt":"Let $G$ be a simple connected graph of order $n$ and $D(G)$ be the distance matrix of $G.$ Suppose that $\\lambda_{1}(D(G))\\geq\\lambda_{2}(D(G))\\geq\\cdots\\geq\\lambda_{n}(D(G))$ are the distance spectrum of $G$. A graph $G$ is said to be determined by its $D$-spectrum if with respect to the distance matrix $D(G)$, any graph with the same spectrum as $G$ is isomorphic to $G$. In this paper, we consider spectral characterization on the second largest distance eigenvalue $\\lambda_{2}(D(G))$ of graphs, and prove that the graphs with $\\lambda_{2}(D(G))\\leq\\frac{17-\\sqrt{329}}{2}\\approx-0.5692$ are de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04225","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"}