{"paper":{"title":"On the $g$-extra connectivity of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sun-Yuan Hsieh, Yaping Mao, Zhao Wang","submitted_at":"2019-04-13T11:14:21Z","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 $g$-extra connectivity of $G$. A subset of vertices $S$ is said to be a \\emph{cutset} if $G-S$ is not connected. A cutset $S$ is called an \\emph{$R_g$-cutset}, where $g$ is a non-negative integer, if every component of $G-S$ has at least $g+1$ vertices. If $G$ has at least one $R_g$-cutset, the \\emph{$g$-extra connectivity} of $G$, denoted by $\\kappa_g(G)$, is then defined as the minimum cardinality over all $R_g$-cutsets of $G$. In t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06527","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"}