{"paper":{"title":"Spectral characterization of the complete graph removing a path of small length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lihuan Mao, Sebastian M. Cioab\\u{a}, Wei Wang","submitted_at":"2018-04-23T07:05:26Z","abstract_excerpt":"A graph $G$ is said to be \\emph{determined by its spectrum} if any graph having the same spectrum as $G$ is isomorphic to $G$. Let $K_n \\setminus P_{\\ell}$ be the graph obtained from $K_n$ by removing edges of $P_\\ell$, where $P_\\ell$ is a path of length $\\ell-1$ which is a subgraph of a complete graph $K_n$. C\\'{a}mara and Haemers~\\cite{MC} conjectured that $K_n \\backslash P_{\\ell}$ is determined by its adjacency spectrum for every $2\\leq \\ell \\leq n$. In this paper we show that the conjecture is true for $7\\leq \\ell \\leq9$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08263","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"}