{"paper":{"title":"On the $g$-good-neighbor connectivity of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jichang Wu, Sun-Yuan Hsieh, Yaping Mao, Zhao Wang","submitted_at":"2019-05-24T15:28:45Z","abstract_excerpt":"Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network $G$. In 1996, F\\`{a}brega and Fiol proposed the $g$-good-neighbor connectivity of $G$. In this paper, we show that $1\\leq \\kappa^g(G)\\leq n-2g-2$ for $0\\leq g\\leq \\left\\{\\Delta(G),\\left\\lfloor \\frac{n-3}{2}\\right\\rfloor\\right\\}$, and graphs with $\\kappa^g(G)=1,2$ and trees with $\\kappa^g(T_n)=n-t$ for $4\\leq t\\leq \\frac{n+2}{2}$ are characterized, respectively. In the end, we get the three extremal results for the $g$-good-neighbor connectivity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11254","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"}